control strategy investigation for a down- scaled forwarder

INDEGREE PROJECT MECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

,STOCKHOLM SWEDEN 2017

Control Strategy Investigation for a Down-Scaled ForwarderRefinement, Testing and Analysis

ANQING DUAN

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT

Examensarbete MMK 2016:99 MDA 571

Control strategy investigation for a down-scaled forwarder

Anqing Duan

Godkänt 2017-06-15

Examinator Jan Wikander Handledare Lei Feng

Uppdragsgivare Skogforsk

Kontaktperson Olle Gelin

Sammanfattning Den dominerande metoden för att skörda träd i Norden är kortvirkesmetoden. Kortvirkesmetoden realiseras av två maskiner: en skördare som används för avverkning av träden och en forwarder som används för att transportera stockarna till en väg som är tillgänglig för lastbilar. För att öka produktiviteten är en möjlig lösning att öka forwarderns körhastighet. Detta kommer dock att bidrar till att operatören utsätts för större vibration och att marken utsätts för större däcktryck. För att lösa ovanstående problem har en sexhjulig forwarder med hjulupphängning i pendelarmar tidigare utvecklats där varje hjul styrs individuellt av en motsvarande hydraulmotor. Med tanke på att genomförande av fälttester på den verkliga forwardern skulle bli tids- och resurskrävande, har tidigare en 1: 5 nedskalad forwarder tillverkats för att underlätta forskningen. På grund av storleksbegränsningarna ersattes de hydrauliska motorerna med linjära cylindrar samt gjordes en del andra konstruktionsändringar. Arbetet med denna avhandling är att ytterligare förfina den nedskalade forwardern med fokus på en 3D modellerings- och animeringsmiljö. Styrstrategin som föreslås är baserad på kinematik. Den föreslagna regleralgoritmen kan balansera den simulerade nedskalade forwardern genom att lösa ett linjärt optimeringsproblem i realtid. Begränsad av sensorprestanda och filteralgoritmer testas endast en förenklad kinematikreglering i simuleringen och i den verkliga nerskalade forwardern. Det kan ses i simulering att både pitch- och roll-vinklar kan minskas kraftigt även med den förenklade reglermetoden vid körning genom Skogforsks standardprovbana. Stabilitetsanalysmetoden för den nedskalade forwardern diskuteras också i denna avhandling. Huvudbidraget från detta examensarbets består i att en annan synvinkel presenterats jämfört med föregående arbeten när det gäller förslag till nya fungerande styrstrategier.

Master of Science Thesis MMK 2016:99 MDA 571

Control strategy investigation for a down-scaled forwarder

Anqing Duan

Approved 2017-06-15

Examiner Jan Wikander

Supervisor Lei Feng

Commissioner Skogforsk

Contact person Olle Gelin

Abstract The predominant method of trees harvesting in Nordic countries is cut-to-length logging (CTL). CTL is realized by two machines: a harvester which is used for felling the trees, and a forwarder which is used for transporting the logs to a road accessible by trucks. To increase the productivity, one possible solution is to increase the forwarder driving speed. However, this will make the operator exposed to larger vibration and cause bigger tire-ground pressure. To solve the abovementioned problems, Skogforsk developed a six-wheel pendulum arm suspended forwarder with each wheel of the forwarder controlled individually by the corresponding hydraulic motor. Given that conducting the field tests on the real forwarder will be time consuming and inconvenient, a 1:5 down-scaled forwarder was manufactured previously to facilitate the research. Due to the size limitation, the hydraulic motors are replaced with the linear actuators besides a few other design changes. The work of this thesis is to further refine the down-scaled forwarder with the focus on implementing the control system. The forwarder is modeled using Sim which provides a 3D animation modelling environment. The control strategy is proposed in a perspective of kinematic control. The proposed control algorithm can balance the down-scaled forwarder orientation by solving a linear optimization problem in real time. Restricted by the sensors implementation and filter algorithms, only a simplified kinematics control is tested in the simulation and the real down-scaled forwarder. It can be seen in simulation that both the pitch and roll angle can be reduced greatly by driving through the Skoforsk standard test track with the simplified control method. Stability analysis method for the down-scaled forwarder is also discussed in this thesis. The main contribution of this thesis will be indicating a different point of view from the previous work in terms of control strategy proposal.

Acknowledgement

First of all, I would like to express my gratitude to Ulf Sellgren and Skogforsk rep-resentatives, without whom I will not be able to have this great thesis opportunity.

Second, I really appreciate the guidance from my supervisor Lei Feng. In additionto technical details, I think the most important thing I have learned from himis rigorous working attitude towards research. I would also like to thank StaffanQvarnström for his help on the hardware.

Last but not least, I am really thankful for the support from my colleagues YuchaoLi, Zhen Li and Qingxiao An. I will never forget the days when we worked together.

Nomenclature

Abbreviations

Symbol DescriptionWAAV Wheeled actively articulated vehicleLQ Linear quadraticLQG Linear-quadratic-GaussianPID Proportional–integral–derivativeMPC Model predictive controlIMU Inertia measurement unitPD Proportional–derivativeRMS Root-mean-squareECU Electronic control unitFR Front rightFL Front leftMR Middle rightML Middle leftBR Back rightBL Back leftCoM Center of mass

Contents

1 Introduction 1

1.1 Background and Problem Description . . . . . . . . . . . . . . . . . . 1

1.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Method Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Expected outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Frame of Reference 7

2.1 Suspension Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Brief Survey on Active Suspensions . . . . . . . . . . . . . . . . . . . 9

2.3 Wheeled Actively Articulated Vehicle . . . . . . . . . . . . . . . . . . 9

2.4 Vehicle Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.1 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.2 Kinematics Model . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4.3 Model Environment . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Modelling Approaches and Control 19

3.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Linear Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.2 Pendulum Arm . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.3 Test Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.4 Wheel-Track Interaction . . . . . . . . . . . . . . . . . . . . . 22

3.2 Control Strategy Proposal . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Kinematic Control . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Simplified kinematic control: On-off Strategy . . . . . . . . . . 26

3.2.3 PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Implementation 35

4.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Hardware List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 IMU Filter Algorithm Analysis . . . . . . . . . . . . . . . . . . . . . 38

5 Results 41

5.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1.1 Tilt Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1.2 Tire Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Model verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 Future Work and Recommendations 53

6.1 Faced Troubles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Bibliography 57

Appendices

Chapter 1

Introduction

This chapter introduces the background of the thesis work, describes the problem tobe solved, states the purpose and delimitations, and proposes the selected methodas well as the expected outcomes.

1.1 Background and Problem Description

The predominant harvesting method used in Scandinavian countries is cut-to-lengthlogging (CTL), which is based on a two-machine solution: a harvester and a for-warder [1]. The harvester is used for felling, delimbing and bucking trees while theforwarder carries the logs from the harvesting area to a roadside loading area wherethey can be picked up by a truck.

In order to stay competitive, the Swedish logging industry needs to increase theproductivity by 2% to 3% per year [2]. One main solution to improving the produc-tivity is to increase the forestry vehicle driving speed. However, if an off-road vehicledrives through a rough terrain at a high speed, the operator will be exposed to astrong vibration. It has been shown that individual lifetime exposure to the whole-body vibration may play an important part in the evaluation of health effects [3]. Inaddition, forestry machines are usually very heavy, the usage of them may harm thefragile and irreplaceable landscapes, leading to erosion and soil compaction, whichthen will affect water absorption and soil permeability [4].

In an endeavor to solve these problems, Skogforsk [5], the forest research institute ofSweden, has built a full-scale forwarder prototype called XT28 as shown in Fig. 1.1.This prototype uses hydraulic pendulum arm suspension for each of its six wheels.The pendulum arm suspension can be controlled individually to drop and lift itscorresponding wheel. Therefore, the off-road vehicle will be leveled when drivingthrough the rough terrain with bumps or pits. By doing so, the operator should havebetter driving comfort since the vehicle can balance itself. Also, the soil damagewill be reduced by actively distributing tire-ground pressure among six wheels.

1

CHAPTER 1. INTRODUCTION

Figure 1.1: XT28 PrototypeTo facilitate the research on the XT28 prototype, a physical 1:5 downscaled for-warder (Fig. 1.2) was realized previously [6]. With the help of the down-scaledprototype, it is much more economic and time saving to test specific features orfunctions instead of driving a full-scaled version. Some relevant experiments haveshown how a scaled vehicle system can be used to facilitate the prototyping of vehiclecontrol systems [7].

Figure 1.2: Down-scaled Prototype

1.2 Purpose

The general context of this thesis work is to further refine the down-scaled forwarderwhich has been developed previously, yet without any control system implemented.The specific purpose of this thesis work is to investigate a suitable control strategyand manage to implement it on the down-scaled forwarder so that the active sus-pension system would function to keep the vehicle body as horizontally stable as

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possible while reducing the tire-ground pressure. The control effects of the proposedcontrol strategy shall be verified by driving the down-scaled forwarder through theSkogforsk standard test track. The specification of the test track is shown in Fig.1.3.

Figure 1.3: Skogforsk Test Track SketchTo illustrate the vehicle dynamic behaviour, the coordinate system and namingconvention are introduced in Fig. 1.4 from [8].

Figure 1.4: Vehicle Coordination SystemBased on the abovementioned, the research question of the thesis is formulated as:

How to control a down-scaled forwarder so that it can beep balanced when drivingthrough a test track?

To answer the research question, this thesis should not only adapt and advance theprevious control method used on the full-scale forwarder but also prove their utilityon the down-scaled version with real experiments. Especially model check will beprioritized since it has never been conducted before while it serves as the foundationthat the following control system implementation will base on.

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1.3 Delimitations

Considering the limited time and the complexity of the project, there are someinevitable limitations to be defined so that it is reasonable to reach the final goalsand the bottom line of the project will be secured.

For the vehicle dynamic behaviour improvement, the only coordinates to be im-proved are pitch and roll axis. The test environment is restricted to the Skogforskstandard test track and the driving speed is set to be a constant value. Also,the control system to be implemented in practice would only be the one with thebest performance in simulation. It should be noted that the down-scaled forwarderhanded over to us has one wheel malfunctioning, which may not be a problem inmodel simulation but could affect real implementation.

When building the forwarder model, some assumptions are made to keep the modelsimplified but without the loss of validity. The sensors used in simulation are con-ceived to be sufficiently precise without any noise considered although in reality theyare not. Similarly, the linear actuator model is conceived ideal as well, i.e. fromvoltage input to the displacement output is an ideal integrator regardless of loadinterruption which can be compensated by required current in the circuit. For thefull scaled forwarder, the steering joints of separate vehicle parts are rigid. However,due to the structure deficiency and chosen materials properties, the steering jointsof the down-scaled forwarder are pliable, which implies that when going throughthe tough terrain, tilt degree of the vehicle would be absorbed by the flexibility ofthe steering joints to some extent. While in the down-scaled forwarder model, thesteering joints would be still considered rigid. In addition, since there will not be anymodel parameter identification conducted, the parameter values used in the modelare chosen within the usual range.

1.4 Method Description

The work procedure of this thesis will follow the general V-model. Verificationand validation play an very important role in progressing the project. The verybeginning task of the project following the literature review is to build the down-scaled forwarder model. This process includes selecting a proper model environment,making reasonable assumptions and considering to set convenient interfaces for thesubsequent proposed control systems.

With the chosen model environment, the built model should be as concise as possiblebut without the loss of necessary accuracy. Model checking will be conducted oncethe model is finished. Two sets of data from model simulation and real experimentsshould coincide with each other within allowable deviation. If model checking man-ifests the model is not trustful enough, the model will be rebuilt or fixed until themodel is usable, so building model is an iterative process. This is to make sure that

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the control system can be implemented on a reliable model since it is assumed to betime consuming and difficult to fix the model and adapt the control systems in themeanwhile.

Until an acceptable model is built, different control strategies would not be tested insimulation. The testing order had better start with the easiest one. After evaluatingtheir control performance quantitatively, the one with the best performance will bechosen to be implemented on the real down-scaled forwarder, where related hardwarewill be prepared and deployed. The final result will be compared with the simulationand the conclusion will be drawn.

Due to the potential hardware restriction, the bottom line of this project would keepemphasis on building the model and control strategies comparison in simulation.

1.5 Expected outcomes

To reach the purpose of the thesis work, the following items shall be achieved ac-cordingly as the expected outcomes:

• Building the downscaled forwarder model in Simscape Mulitibody.

• Investigation, simulation and evaluation of different control strategies.

• Model validation by comparing the simulation results with the empirical data.

• Implementing the selected control strategy in practice.

• Documentation of the project.

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6

Chapter 2

Frame of Reference

This chapter supplements the research background to the thesis further in a detailedway and shows literature review results including theoretical knowledge and engi-neering techniques. Innovations of the thesis will be based on the frame of reference.

2.1 Suspension Systems

Vehicle suspension systems basically consist of tire, spring, shock absorber and link-ages to transmit and filter all forces between body and road [9]. The spring is usedto carry the body-mass and isolate the body from road disturbances, which willcontribute to ride comfort. The damper is the damping of body and wheel oscilla-tions, where the avoidance of wheel oscillations directly refers to ride safety. Sincethe vehicle suspension system is responsible for ride comfort and safety, it plays animportant role in modern vehicles [10].

Generally speaking, suspension systems can be categorized into passive suspensions,semi-active suspensions, and active suspension systems. A passive suspension has nosource of energy. An active suspension incorporates extra energy sources to refinethe compromise. The idea of a semi-active suspension is to replace active forcegenerators with continually adjustable elements which can vary or shift the rate ofenergy dissipation in response to an instantaneous condition of motion [11].

The suspension type used on the down-scaled forwarder is active suspension. Itis widely accepted that an active suspension system is an effective way to improvesuspension performance. The abstract structure for general active suspension systemis shown as Fig. 2.1.

7

CHAPTER 2. FRAME OF REFERENCE

Figure 2.1: Active Suspension Sketch for A Quarter-Vehicle Model

Fig. 2.2 shows the active suspension system structure used on the forwarder. Theenergy source is supplied by the hydraulic actuator. The left hub is fixed to thevehicle body frame and is free to rotate. The right hub is attached to a wheel andthe wheel can move in an arc curve. In total the forwarder has six of this module.

Figure 2.2: Pendulum Arm System

For the down-scaled version, all the components remain the similar structure exceptthat they are realized in a down-scaled size. Due to the size problem, it is not viableto use a down-scaled hydraulic actuator anymore. Therefore, the hydraulic actuatoris replaced with a linear actuator which can also allow the stroke to move in a linearway. It should be expected that by doing such modification, the two suspensionsystems could have two different working principles in that the control signals havedifferent physical meaning. For the active suspension of the full-scaled forwarder,the control signal is given as force, i.e. the wheel will rotate under the exertedforce by the hydraulic piston regardless of its position. While for the down-scaledforwarder, the control signal is given as position, i.e. the rotation of the wheel issubject to the position of the piston. Theoretically, the linear actuator can offerenough support force due to its natural self-lock mechanism. If the wheel forcesthe piston to move backwards, the linear actuator would be damaged. In fact, theexternal force on the wheel can not even reduce the piston speed lower than thespeed at the maximum thrust. The obviously different properties of the two controlsignals will influence the control system greatly.

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2.2 Brief Survey on Active Suspensions

Active suspension control strategies investigation is a very popular topic that avariety of research has been conducted on. Many existing control strategies havebeen proven to be applicable for active suspension control using quarter-, semi- orfull vehicle models.

Krtolica et al. managed to use optimal control to control active suspension systemby completing an analytical solution of the related fourth-order LQ problem basedon a half-car model [12]. Rao et al. presented a novel fuzzy-logic-based control usinga new look-up table for the rule base of fuzzy logic for the vehicle-active suspensionof a quarter car [13]. The proposed fuzzy logic controller can enhance comfort inriding faced with uncertain road terrains by reducing the vehicle vibration and dis-turbance considerably. Yamashita et al. used H∞ control theory for a full vehiclemodel to achieve robust performance and their closed-loop system has been evalu-ated in shaking and driving experiments [14]. Alleyne designed a nonlinear adaptivecontroller for the active suspension where a standard parameter adaptation scheme,based on Lyapunov analysis, is introduced to reduce the error in the model sincethe controller relies on an accurate model of the suspension system [15]. Mehra etal. used model predictive control and preview information for the active suspen-sion, manifesting that MPC controller performs better than LQG and is tolerant tosignificant amounts of noise on the preview information [16].

2.3 Wheeled Actively Articulated Vehicle

In addition to the perspective of controlling the down-scaled forwarder by treatingthe pendulum arms as active suspension, there are also evidences showing thatthe down-scaled forwarder behaving quite similar to a wheeled actively articulatedvehicle [17]. Some of the typical wheel leg robots are studied as well.

Bill Ross at the Robotics Institute at Carnegie Mellon built an agile six-legged workrobot as Fig. 2.3. The robot has high power density and can work in tight andcomplex space by being equipped with diesel-electric hybrid drive. All six legs haveindependent wheel drive motors which can help the robot operate in even the mostchallenging environments [18].

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Figure 2.3: Agile Six-Legged Work RobotFig. 2.4 shows another wheel leg robot named Hylos robot. A combined postureand trajectory control allows to specify the locomotion task in terms of: first thepath tracking control and secondly the posture reconfiguration control based on theinverse velocity model of the vehicle [19]. The robot is capable of reducing the pitchand roll angle when running through the inclined ground.

Figure 2.4: Hylos RobotThe Jet Propulsion Laboratory planetary rover family is a widely recognized familyof passive leg-wheel platforms, for example, the Rocky 7 Rover shown in Fig. 2.5.The Rock 7 Rover is capable of long traverses, autonomous navigation, and scienceinstrument control. The rover has a steerable wheel at the end and a smaller rockerat the other end. A lever can constrain the motion of the main rockers with itstwo ends attached to the main rockers. This design can provide an importantcharacteristic: one wheel can be lifted vertically while other wheels remain in contactwith the ground [20].

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Figure 2.5: the Rocky 7 RoverA planetary rover named NEXUS from the Tohoku University is shown in Fig. 2.6.It has 6 wheels connected by a Rocker-Bogie type suspension link system. Themodelling of the rover is based on the tire-soil mechanics and the motion dynamicsof the vehicle load. Especially the traction factor, which is the ratio of the tangentand normal forces on a tire is derived in [21].

Figure 2.6: NEXUSFig. 2.7 shows locomotion concept of CRAB consisting of two parallel bogies linkedwith an articulated rocker. An overview of the software tools that can be used forperformance evaluation of all-terrain robots and the performance optimization tool(POT) is introduced in [22]. The performance of the CRAB is evaluated with theproposed POT.

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Figure 2.7: CRAB at ETH

2.4 Vehicle Model

Building the model of the object to be controlled always plays an important role inthe control strategies investigation. Proper mathematical model should be concludedwhich can reflect input-output relationship as realistic as possible with reasonablemodel complexity. Consequently, model environment would be chosen accordingly.

To start with, a proper mathematical expression would be derived for the down-scaled forwarder. There are two viewpoints from which the mathematical modelcan be derived: dynamics model and kinematics model.

2.4.1 Dynamic Model

The dynamic vehicle model will be built according to the Newton’s second law.Different from prevalent vehicle model where vehicle dynamic behaviour is drivenby the forces from active suspension system composed of mass, damper, spring andexternal actuators, in this project, only the ground-tire force is considered as thefactors causing the vehicle dynamic behaviour in that the suspension system of thedown-scaled forwarder is quite rigid and multibody system can then be simplifiedas a whole rigid body except the tires.

The tire-road interaction dynamnics can be achieved by magic formula [23]. Itsgeneral form is expressed as

Fx = f(k, Fz) = FzDsin(C · arctan[Bk − E[Bk − arctan(Bk)]]) (2.1)

where B, C, D and E are dimensionless denoting stiffness, shape, peak and curvature;Fx the longitudinal force; Fz the vertical force and k the wheel slip. The slope of fat k = 0 is BCD · Fz.

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Figure 2.8: An Articulated Vehicle SketchSimilar to [21], equation of motion depicting an articulated model as Fig. 2.8 butwithout considering steering part is given in Eq. 2.2.

H

v0ω0

θsθw

+ C =

F0

N0

ns

nw

+ JTFe (2.2)

where

H : inertia matrix for the entire system composed by the inertia property of eachbody

C : non-linear velocity-dependent term

v0 : translational velocity of the base body

ω0 : rotational velocity of the base body

θs : suspension angle

θw : rotational angle of the wheel

F0 =(0, 0,−m0g)T : forces exerting on the base body

N0 : moments exerting on the base body

ns : torque on the suspension joints

nw : driving torque of the wheels

J : Jacobian matrix

Fe =(fTw1, ..., f

Tw6): tire forces

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2.4.2 Kinematics Model

When a mobile robot has active revolute or prismatic joints, it should be consideredto build a kinematics model. An assumption here is that the wheels or legs makepoint contact with the ground.

2.4.2.1 General Kinematics Reconfigurability

The goal of kinematic reconfigurability is to improve robot performance by modi-fying the robot joint variables to optimize a user-specified performance index [24].Kinematic reconfigurability can be devided into two cases: internal reconfigurabilityand external reconfigurability.

In internal reconfigurability the link-terrain contact points remain fixed relative tothe terrain during the reconfiguration. When it comes to a wheeled robot, thewheel should keep actively controlled without rolling. The mobility of internallyreconfigurable robot can be calculated by the Grubler mobility criterion:

F = 6(L− J − 1) +

j∑i=1

fi (2.3)

where j is the number of joints, l is the number of links including the ground, and fiis the number of constraints for each joint i. The terrain profile does not influencethe reconfiguration process of an internally reconfigurable robot. Therefore, onlyusing the knowledge of robot kinematics is enough to formulate an optimizationproblem and a globally optimal solution is possible to find.

In externally reconfigurability the link-terrain contact points will move relative tothe terrain during the reconfiguration process. Mobility analysis of an externallyreconfigurable robot is different from that of an internally reconfigurable robot.Wheel-terrain contacts must be treated as higher order pairs. Since the reconfigura-tion process involves terrain profile, a globally optimal solution will not be possibleto find without knowing the terrain profile. However, the local wheel-terrain con-tact angle can be estimated. An optimization problem can be formulated with aconstraint that the reconfiguration process only results in small displacement of thecontact points with respect to the terrain.

On-line kinematic reconfigurability has three steps in an ad hoc order:

• Evaluation of the robot configuration denoted with pitch and roll, wheel-terrain contact angles as well as joints position using on-board sensors.

• Computation of a kinematic configuration which can optimize a given perfor-mance index.

• Motion from the current robot configuration to the optimal configuration.

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2.4.2.2 Stability Analysis

The control of robotic system under stability margin condition was mainly addressedin the field of legged locomotion. Different mechanical stability margins were definedduring past research on walking machines. It can be considered that roughly sixtumble stability criteria for walking vehicles were proposed as follows [25]:

1) "Stability Margin": It evaluates the distance between the projection of thecenter of gravity on the ground and the border of the polygon formed by thesupporting feet of the walking vehicle on the plane.

2) "Tumble Stability Margin": When the walking vehicle tumbles around the lineconnecting two support feet, it evaluates the absolute value of the momentdivided by its weight which generates around the line to avoid tumbling. Itcorresponds to the "Stability Margin" ignoring the dynamic effect when thewalking vehicle is on the level ground.

3) "Gradient Stability Margin": It evaluates the inclination of the walking vehicleat which it starts tumbling owing to gravity, when it gets inclined little by littlefrom the level ground.

4) "Tipover Stability Margin": It is similar to the criterion of the "GradientStability Margin," but all the external forces including gravity are consideredto work on the center of gravity of the walking vehicle.

5) "Energy Stability Margin": In the process of tumbling, the center of gravitypasses over the point at which it possesses the maximum potential energy underthe field of gravity. This criterion evaluates the stability by the magnitude ofthe difference between its maximum potential energy and its initial one.

6) "Dynamic Energy Stability Margin": It is similar to the criterion of the "En-ergy Stability Margin," but all the external forces including gravity are con-sidered to work on the center of gravity of the walking vehicle.

In particularly, details about the "Stability Margin" is reviewed here since it ispersistent to the down-scaled forwarder and easy to realize [26]. To illustrate, ageneral mobile robot is defined as Fig. 2.9. The robot has m wheel-terrain contactpoints pi with i = 1, ...,m numbered in ascending order in a clockwise when viewedfrom above. The lines joining the terrain-contact points are referred to as tipoveraxes and denoted ai, where the ith tipover axis is given by:

ai = pi+1 − pi, i = {1, ...,m− 1}, (2.4)am = p1 − pm. (2.5)

Tipover axis normals li that intersect the center of mass can be described as:

Ii = (1− aiaiT )pi+1, (2.6)

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where a = a/ ‖ a ‖. Stability angles can then be computed for each tipover axis asthe angle between the gravitational force vector fg and the axis normal li:

γi = σicos−1(fg · Ii), i = {1, ..., n}, (2.7)

with

σi =

{+1, (Ii × fg) · ai < 0

−1, otherwise(2.8)

The overall vehicle stability angle is defined as the minimum of the i stability angles:

α = min(σi), i = {1, ..., n}. (2.9)

When α 6 0 a tipover instability is occurring. Thus, the goal of stability-basedkinematic reconfigurability is to maintain a large value of α. It should be noted thatwhen there is applied forces such as a manipulator on its environment, the stabilitycalculation should take external force into account.

Figure 2.9: Stability Definition Diagram2.4.2.3 Kinematic Control

A kinematic control approach is proposed in order to modify the robot configurationand relocate its center of mass to enhance the system mobility [27]. The idea of thekinematic control is to send command in terms of robot joints velocity to adjust thecontact points. Without loss of generality, assuming that the proposed control onlyactuates in the vertical component of each contact point, the differential kinematicsof a robot with 1 DOF for leg is given by:

vzi = jzi(θi)θi (2.10)

where vzi is the linear velocity of the contact point along vertical direction, jzi thevertical component from the system Jacobian matrix, which can be obtained fromthe forward kinematics of the mechanism, θi the position and θi the velocity of the

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joint i. Considering θi is the control input ui, the following control law can beproposed:

ui = jzi(θi)−1vzci (2.11)

where vzci is the commanded linear velocity in the vertical axis of the contact point.The control law vzci can be calculated from the following objectives:

Ground Clearance Control

The control law should guarantee the ground clearance by following a given referenceconsidering the robot is more stable when it is closer to the ground but should alsoremain a minimum safety reference.

Orientation Control

The control law should cancel pitch and roll angles and keep the robot body in thehorizontal plane.

Traction Control

The control law should distribute the load forces evenly among all wheels.

Stability Control

The control law should maximize the stability of the robot in terms of some stabilitycriterion such as stability margin.

Multiple Objectives Control

The control law can be given to meet multiple objectives stated above by combiningthe different joint commands.

2.4.3 Model Environment

For vehicle dynamic analysis, there are several modelling platforms. For instance,Adams is a popular multibody dynamic simulation software equipped with Fortranand C++ numerical solvers [28]. It has several advantages including a user friendlygraphical user interface (GUI), automatic assembly of Equations of motion and arobust and efficient integration algorithm for differential equations. The Adamssoftware uses generalized Cartesian coordinate and hence the assembled equationsare a set of differential algebraic equation of index three [29]. There are also someother vehicle dynamic modellling software such as CarSim [30] and veDYNA [31].

Another powerful modelling software is Matlab. It is possible to realize a statespace model using Simulink. And there is previous work realizing a state spacemodel for the forwarder [32]. Also, it is possible to use Simscape/multibody inMatlab environment for the model simulation. Similar model was built with thefirst generation Simmechanics [33].

17


Given that it is needed to implement control system for the down-scaled forwarder ata later phase, the interface between Adams and Matlab will be required. Therefore,it will be more convenient to build the model in Matlab directly. In addition, a statespace model will not be chosen since it can only reflect continuous behaviour of adynamic system. The wheels of the forwarder could lose contact with the test trackeasily. This hard non-linearity property makes linear model, such as state spacemodel, not feasible anymore. Thus the best choice would be building a 3D modelusing Simmechanics. The newest second generation of Simscape is chosen as themodelling environment.

18

Chapter 3

Modelling Approaches and Control

This chapter presents the insights on the proposed simulation model by showing themodel methods for the key components of the forwarder. Some important specifi-cations on the forwarder are also given in this chapter.

3.1 Simulation Model

The down-scaled forwarder model is realized by MATLAB/Simscape MultibodyTM.MATLAB/Simscape Multibody can provide an automatically generated 3-D anima-tion so that the built simulation model can be visualized. This is especially helpful toanalyze complex dynamic systems such as robots, vehicle suspensions, constructionequipment etc.

3.1.1 Linear Actuator

The real linear actuator is shown as Fig. 3.1 and the related data specification is asAppendix.

Figure 3.1: Linear actuator

The Simulink model blocks layout and its animation result for the linear actuatormodel are shown in Fig. 3.2.

19

CHAPTER 3. MODELLING APPROACHES AND CONTROL

(a) Simscape Blocks layout

(b) Animation result

Figure 3.2: Linear actuator modelThe input-output for the linear actuator are the voltage and the stroke speed re-spectively. The ideal relationship between the input and the output is linear withthe limitation of maximum voltage 24V versus maximum stroke speed 15mm/s.The model scheme as well as its simulation results are shown in Fig. 3.3. The idealrelationship should be linear when the load force is within maximum allowable staticforce. Disturbances from the external load force variation will be compensated bythe current.

Figure 3.3: Ideal linear actuator input-output relationship

20


3.1.2 Pendulum Arm

The suspension system is composed of six pendulum arms with each one bridgingthe vehicle body and one wheel. There are two types of pendulum arms due tosymmetry. We can take one for example as shown in Fig. 3.4.

(a) CAD model

(b) Simscape animation

Figure 3.4: Pendulum arm suspension systemThe density value of the material in the simscape model is chosen considering theweight of the linear actuators as well as the steel pendulum arm and hubs. Thebearing used in the real model is realized by the joint block between the compo-nents. The maximum velocity and stroke limit position of the piston is saturated inaccordance with the real linear actuator.

3.1.3 Test Track

Skogforsk uses standard test track as shown in Fig. 3.5 to test the suspensionperformance of the forwarder. In order to save computation power, only part of thetest track is modeled since the eliminated part is highly repetitive. In fact, there areonly three types of bumps sharing similar shape but with different sizes. The sketchof the modeled test track road profile is as shown in Fig. 3.6. The bump width iswide enough to hold the wheels at each side. The bump dimension can be obtainedfrom the coordination which is calibrated in mm.

21


Figure 3.5: Skogforsk standard test track

Figure 3.6: Test track bump profile

3.1.4 Wheel-Track Interaction

The wheel and track interaction is realized by Simscape Multibody Contact ForcesLibrary [34]. The selected basic elements for representing the interaction betweenthe wheels and the test track are sphere-plane block and sphere-tube block. Sphere-plane block is responsible for the interaction between the wheel-ground and wheel-bump slope. Sphere-tube block is responsible for the interaction between the wheeland the bump peak.

The sphere to sphere contact force block diagram with its specification is shown asFig. 3.7. For diemnsions, the sphere radius and follower radius are required to beset. For contact, contact stiffness and contact damping are parameters to be set.For coefficient of kinetic friction and coefficient of static friction as well as velocitythreshold are required to be set.

22


Figure 3.7: Contact Force Block Mask

3.2 Control Strategy Proposal

The control strategy proposed for the down-scaled forwarder active suspension sys-tem should take linear actuator characteristics into consideration. Since the selectedlinear actuator has a highly linear property between the input voltage and the outputstroke speed, it can be controlled comparatively easily. Advanced control strategiesused for the real forwarder active suspension system composed of hydraulic cylin-ders could be deprived. To start with, kinematic control as mentioned in the abovesection would be tried firstly.

3.2.1 Kinematic Control

There are two purposes for the kinematic control: 1) keep the forwarder in horizontalbalance so that the driver can feel comfortable; 2) make sure that the number of thewheels that are in contact with the ground is as big as possible. Before implementingkinematic control, there are some assumptions made:

Assumption 1 : The wheel-terrain contact is point contact.

Assumption 2 : Wheel-terrain contact angle keeps constant when the forwarder isdriving or moving its joints.

Assumption 3 : There is no slip between the wheel and the terrain.

Assumption 4 : There are always at least three wheels in contact with the ground.

23


To illustrate the proposed kinematic control method, a sketch of the forwarder withassociated frames is shown in Fig. 3.8. The velocity expression is denoted with itsreference frame on the super script:

• Ro: the reference ground frame or world frame

• Rf : the main forwarder platform frame attached to the center of gravity

• Rwi : the ith wheel frame without rotation attached to the wheel center

The linear actuator piston position for each wheel is denoted as li and the rollingangular velocity magnitude for each wheel with respect to the world frame is denotedas ωr

oi , i = {1, .., 6}. The ith tire-terrain contact angle in the vertical plane is αo

i .The ith pendulum arm angular velocity ωf

i with respect to the forwarder referenceframe is expressed as

ωfi = Ji(li)li (3.1)

where Ji is the Jacobian matrix for the ith wheel. The vertical component of thependulum arm end point on the vehicle body side vzoi with respect to the world framereference is of interest since it contributes to the forwarder orientation directly. vzoiis a linear combination resulting from two parts: contact points vertical movementvcz

oi and pendulum arm end point vertical movement vpzwi due to the pendulum arm

rotation and the pitch and roll angle of the forwarder:

vzoi = vcz

oi + vpz

wi (3.2)

The contact points movement vczi can be calculated with wheel rolling speed andtire terrain contact angle.

12 3

4

5

6O

RO

xO

yO

zO

Rwi

Rf

Figure 3.8: Sketch of Forwarder with Associated FramesBefore analyzing the effects of vzoi on the forwarder configuration, it should be notedthat three wheels from both sides are enough to define the orientation of the for-warder. So only three wheels from both sides will be selected to reconfigure the

24


forwarder orientation. The selection criterion is based on tire-terrain pressure value.The wheels with bigger tire-terrain pressure value are preferred since they are con-sidered having bigger chance in contact with the ground during reconfiguration.The wheel in the left side with the maximum tire-terrain pressure is selected andlabeled as a. The wheel in the right side with the maximum tire-terrain pressure isselected and labeled as b. The third selected wheel has the maximum tire-terrainpressure value in the remaining wheels. The total reconfiguration of the forwarderis considered a superposition of the three wheels effects.

1

2

3

4

5

6

α

β

Figure 3.9: Top View of the ForwarderThe forwarder orientation is expressed with pitch and roll angles. It can be consid-ered a unit vector is fixed upwards perpendicular to the vehicle body so that whenthere is tilt angle, the projection of this unit vector on the horizontal plane is (α, β)as in Fig. 3.9 where α is roll angle and β is pitch angle. Let labc denote the vectororiginating from bc with the end point at a. An optimization problem here is tomake the forwarder go back to balance as fast as possible, so the cost function isformulated as

− (labc × vzoa + lbca × vzob + lcba × vzoc) · (α, β) (3.3)

with the constraint that the other wheels in contact with the ground should be ableto have contact with the ground during reconfiguration:

min(vzoj) 6 vz

oj 6 max(vz

oj) (3.4)

where j indicates the wheel number in contact with the ground, vzoj the compliantspeed as given in Eq. 3.5, min(vz

oj) and max(vz

oj) are calculated from the linear

actuator piston speed range.

vzoj = sgn(ljab ·lcab)

‖ ljab ‖‖ lcab ‖

vzoc+sgn(ljac ·lbac)

‖ ljac ‖‖ lbac ‖

vzob+sgn(ljbc ·labc)

‖ ljbc ‖‖ labc ‖

vzoa

(3.5)

25


The command for the wheels that are in the air should extend the linear actuatorso that the wheel can be put down to contact the ground.

3.2.2 Simplified kinematic control: On-off Strategy

On-off control might be the simplest control strategy. It only serves as a negativefeedback controller in the system. Like a switch, the control signal operates at twostates depending on the sign of the difference of the process variable and the pre-setvalue. However, it could be cheap and effective in quite some circumstances such asfan controlling or temperature controlling [35].

In our case, on and off represent the two directions for the linear actuator. On-offcontrol strategy is employed due to the following reasons. First, in order to make thepitch and row angle get back to zero at the fastest speed, the linear actuators shouldoperate with fully opened at two directions. This will give the forwarder body thefastest rotation speed. Second, there is no overshoot problem for linear actuator. Sothere is no worry about unexpected overshoot caused by the full speed. The linearactuator can stop immediately when giving no input voltage. Third, on-off controlcan be realized easily since it dose not require expensive hardware setup. Controlsignal cold be computed quickly without unnecessary delay.

Figure 3.10: On-off control system operation schemeHowever, there could be some other problems caused by using on-off control strategy.A typical problem is chattering problem arising around the set point. When themeasured controlled variable crosses the set point, there is danger that the controlsignal switches on and off at very high frequency. To avoid chattering problem,deadband is usually used in practical on-off controllers. A deadband, as knownas hysteresis, is a region around the set-point value in which the controller has noaction.

26


Figure 3.11: On-off control system with deadbandWhen the pitch or roll angle is not zero, the linear actuators should operate ac-cordingly. Especially, when the wheel is off the ground, the corresponding linearactuator should extend and put the wheel down in order to make the wheel contactthe ground again regardless of the value of the pitch and roll angle. Each linearactuator operation principles are shown as Table 3.1. Pitch+ represents the frontof the forwarder is higher than the rear of the forwarder and for pitch− vice versa.Roll+ represents the right side is higher than the left side and for roll− vice versa.When programming the real controller, there is a set deadband to avoid chatter, sothat only the tilt angle exceeds than some value the linear actuators would operate.

Table 3.1: Linear actuators operation principle

FL FR ML MR RL RROff the ground + + + + + +Pitch+ + + − − − −Pitch− − − − − + +Roll+ − + − + − +Roll− + − + − + −

From the table it can be observed that the linear actuator operation direction con-flicts when the sign of the pitch angle and roll angle matches in a specific way. Itshould be considered to assign weight coefficients for the control signal from thepitch and roll angle respectively. The coefficients should make sure that the mostsevere situation matters and get the dominance of the linear actuator. Taking theFL wheel as an example, a pseudo control law is given by

27


upitchFL (t) =

{sgn(epitch(t))× umax, |epitch(t)| > Deadbandpitch

0, |epitch(t)| 6 Deadbandpitch(3.6a)

urollFL (t) =

{−sgn(eroll(t))× umax, |eroll(t)| > Deadbandroll

0, |eroll(t)| 6 Deadbandroll(3.6b)

uFL(t) = KpitchFL upitchFL (t) +Kroll

FL urollFL (t) (3.6c)

where umax denotes the maximum control power for the linear actuator to extend atthe limit speed; Deadbandpitch Deadbandroll are introduced pre-set deadband valueto avoid chattering problem as mentioned previously. The final output control signaluFL(t) is computed as a linear combination of upitchFL (t) in terms of pitch angle errorand urollFL (t) in terms of roll angle error with corresponding weight coefficients Kpitch

FL

and KrollFL . The control laws of the wheels FR, RL and RR are similar to that of FL.

The only difference lies on the sign before the maximum control signal umax.

When it comes to the wheels ML and MR, the control law is a bit different becausethe linear actuators always need to contract when the pitch angle is not zero despiteof its sign. It can be interpreted by considering the forwarder like a seesaw. Whenthe pitch angle is not zero, the middle wheels serving as a pivot should reduce theirheight. Therefore the linear actuators at the middle wheels should always contractwhen the pitch angle exceeds the pre-set deadband value. A control law for ML isgiven in Eq. 3.7 and a similar form applies for MR.

upitchML (t) =

{−umax, |epitch(t)| > Deadbandpitch


urollML(t) =

{−sgn(eroll(t))× umax, |eroll(t)| > Deadbandroll

0, |eroll(t)| 6 Deadbandroll(3.7b)

uML(t) = KpitchML upitchML (t) +Kroll

MLurollML(t) (3.7c)

3.2.3 PID Control

Based on the linear actuators operation principles table, it is also possible to imple-ment PID controller for the suspension system. Taking the FL wheel as an example,the proposed PID control law are formulated in Eq. 3.8.

28


upitchFL (t) = Kpitchp_FLe

pitch(t) +Kpitchi_FL

∫ t

0

epitch(τ)dτ +Kpitchd_FL

depitch(t)

dt(3.8a)

urollFL (t) = Krollp_FLe

roll(t) +Krolli_FL

∫ t

0

eroll(τ)dτ +Krolld_FL

deroll(t)

dt(3.8b)

uFL(t) = KpitchFL upitchFL (t) +Kroll

FL urollFL (t) (3.8c)

The control signal for the FL wheel is uFL(t), which is derived from two parts, thecontrol signal upitchFL (t) denoting the pitch side with the pitch error epitch(t) and thecontrol signal urollFL (t) denoting the roll side with the roll error eroll(t). Kpitch

FL andKroll

FL are the weight coefficients to combine the two control signals. The value of thePID coefficients Kpitch

p_FL, Kpitchi_FL, K

pitchd_FL, K

rollp_FL, Kroll

i_FL, Krolld_FL should be selected

accordingly. Similarly we can obtain the PID control law for the remaining wheelsFR, RL and RR. It should be noted that the sign of the PID coefficients should bedecided dependent on the operation principle.

Here the control law form for the wheels ML and MR is different as well. The controllaw is given separately. Taking the ML wheel as an example, the PID control law isgiven by

upitchML (t) =

{−umax, |epitch(t)| > Deadbandpitch


urollML(t) = Krollp_MLe

roll(t) +Krolli_ML

∫ t

0

eroll(τ)dτ +Krolld_ML

deroll(t)

dt(3.9b)

uML(t) = KpitchML upitchML (t) +Kroll

MLurollML(t) (3.9c)

where umax denotes the maximum control signal for the linear actuator to extend.A similar control law can be derived for the MR wheel.

All PID control law only applies when the wheels contact the ground. As long asthere is clearence distance between the wheel and the ground, the correspondinglinear actuator would extend to make the wheel contact the ground again.

Considering the actuator saturates there will be windup in the integrator. In order toavoid windup caused by the integrator of the PID controller, a standard anti-winduptechnique called back-calculation as in Fig. 3.12 is applied to the PID controller.The difference between the output of the controller u and the actuator output usat isfed to the input of the integrator with gain Kt so that when the actuator saturates,the integrated error will be decreased and the controller output can be kept closeto the saturation limit. The feedback gain Kt is responsible for the rate of thecontroller output reset, with a large value giving a short reset time. But gain Kt

cannot be too large since measurement noise can then cause an undesirable reset.A reasonable value for Kt is a fraction of Kd/Kp [36].

29


Figure 3.12: PID Controller with Anti-windupPID parameters selection is conducted based on a simplified and linearized modelwhere the plant is assumed to behave as an integrator with voltage input and errorangle output as shown in Fig. 3.13. It should be noted that the gain of the plantcan vary with pitch and roll as well as the change of the support method for theforwarder. It is considered to use roll angle as the index. Roll angle is more criticalthan pitch since the gravity center projection is closer to the wheels than pitch whensuffering the same tilt angle. The value of the gain is expressed as

Kv_w

voltage for linear

actuator 1s

tilt angle

Figure 3.13: Simplified Model for Plant

Kv_ω =∆Cl

Vmax × wd × tmin

=0.16

24× 0.4× 7.3rad/s · V = 0.0023rad/s · V (3.10)

where ∆Cl is the maximum ground clearance difference between the lowest positionand the highest position; Vmax is the maximum voltage for the linear actuator; wd

is the vehicle width; tmin is the minimum time for the vehicle travel through themaximum ground clearance. In consequence, the block used for tuning the PIDparameters is shown in Fig. 3.14. The selected PID and filter value should giveminimum overshoot and fast response.

30


Figure 3.14: Block Used for Tuning PID

3.3 Simulation results

The influence of the PID value on the output is shown as Fig. 3.15. It can be seenthat when P = 400 and I = 120 the process is fast but without overshoot. Thevalue of D has no effect on the results and its value is chosen as 10.

0 5 10 15 20 25 30

-0.4

-0.3

-0.2

-0.1

0

P = 400

P = 300

P = 500

Offset=0

(a) P Tuning Process with D = 10 and I = 120

0 5 10 15 20 25 30

-0.4

-0.3

-0.2

-0.1

0

I = 120

I = 90

I = 150

Offset=0

(b) I Tuning Process with P = 400 and D = 10

Figure 3.15: PID Tuning Process

31


0 5 10 15 20 25 30

-0.4

-0.3

-0.2

-0.1

0

D = 10

D = 1000

D = 2000

Offset=0

(c) D Tuning Process with P = 400 and I = 120

Figure 3.15: PID Tuning Process (cont.)The Simscape model overview is given in the Appendix. To start with, the pistonsof the linear actuators are set at the middle position lm. This can make sure thatthe linear actuators can handle both situations of extending or contracting with thesame capability. The forwarder running speed is set at v = 45mm/s to mimic thereal forwarder running speed.

The simulation results from on-off control and PID control are given in Fig. 3.16and Fig. 3.17 respectively. From the animation process, it can be observed thaton-off control somehow generates a more swift reaction speed to the bumps thanthe PID control. This can be explained that on-off control in some cases gives thefull power for the linear actuator to operate while the control signal from PID isdependent on the error and thus might not be at its maximum value.

(a) (b)

(c) (d)

(e) (f)

Figure 3.16: On-off control animation results32


(a) (b)

(c) (d)

(e) (f)

Figure 3.17: PID animation resultsDuring simulation, the center of mass of the forwarder tends to become higherafter it comes through the test track. All the linear actuators extend to its longeststate at the end of the simulation. In order to guarantee the center of mass of theforwarder can tend to converge to the level where the linear actuators are at themiddle position, another control rule as in is introduced to adjust the height theforwarder body. It should be noted that the control law will only apply when

|epitch(t)|+ |eroll(t)| <Mangle (3.11)

where Mangle is the threshold value to decide which one should be controlled firstbetween tilt angle and center height. Otherwise the control law will be given as Eq.3.12.

ui =

{sgn(6lm −

∑RRi=FL li)× umax, |6lm −

∑RRi=FL li| > DeadbandCoM

0, else

where i = FL, FR, ML, MR, RL, RR.

(3.12)

As long as the sum of the extension length of all linear actuators∑RR

i=FL li) exceedsthe threshold denoted byDeadbandCoM , the linear actuators would operate to adjustthe forwarder height.

33


When running simulation, it is observed that the forwarder has an obvious longitu-dinal shock when the front actuators extend to a long distance and the front wheelsstart to come through a bump. It is because that the a more vertical pendulum armsat the front of the forwarder will have a higher chance to make the front wheels hitinto the bump when it rotates according to the pitch error. A diagram explainingthis phenomena is as Fig. 3.18. The dashed line represents the motion track of thepeak point at the wheel that when the wheel is rotated by the pendulum arm tocompensate the pitch error. The longitudinal shock happens because of the inter-section between the dashed line and the bump slope. Actually in this situation itis better to put down the front wheels rather than lift them up although the pitchangle here is positive. When going through the bumps, perhaps whether the frontwheels should put down or lift up should be decided by the relative angle of thependulum arms and the bump slope.

Figure 3.18: Longitudinal shock diagram

34

Chapter 4

Implementation

This chapter describes the technical details of the involved hardware and softwarefor real implementation and elaborates the reasons why they are chosen as such.

4.1 System Overview

Figure 4.1: System overviewThe overview of the system is as shown in Fig. 4.1. In the system the controller lieson the center place where the measured data is collected and the control signals arecomputed and sent. The down-scaled forwarder is driven by the EC motors. EachEC motor is controlled by an ESCON speed controller so that they can maintaina constant speed. Current sensors are connected in series with the EC motors sothat the load variation of the wheel can be measured. By doing so, it will be knownwhether the wheel contacts the ground or not. It is expected that the wheel hangsin the air would cause a smaller current in the circuit since the power required todrive an idle wheel is minimum when the input voltage remains constant. In orderto obtain the pitch and roll angle, an inertia measurement unit (IMU) is needed to

35

CHAPTER 4. IMPLEMENTATION

install on the forwarder. Based on the received data from the sensors, the controllerwill send control signals to the linear actuators.

All the signals should be filtered with a low-pass filter to filter out additional noisebefore they are used. The on-board low-pass filter on the Arduino board can beused.

4.2 Hardware List

Involved hardware items are listed as below along with the introductory descriptionon how to set them up.

µ-controller

The chosen µ-controller is Genuino 101 as shown in Fig. 4.2. It is the same prod-uct as Arduino 101 with the exception that it is only available outside the USA.The controller is quite easy to program with open-source code and mature libraries.Genuino 101 can be purchased at an entry-level price. In addition, it has built-in6-axis accelerometer/gyro on the board. This can be used as IMU in our case. Somerelevant technical specifications are as in Table 4.1.

Table 4.1: Technical specifications for Genuino 101

Microcontroller Intel CurieOperating Voltage 3.3V (5V tolerant I/O)Input Voltage (recommended) 7-12VInput Voltage (limit) 7-17VPWM Digital I/O Pins 4Analog Input Pins 6Clock Speed 32MHzFeatures Bluetooth LE, 6-axis accelerometer/gyro

At least two controller are required since there are only 4 PWM pins for each con-troller while it is needed to control six linear actuators with each on connected toone PWM pin. When doing real implementation, three controllers are used and putat the front part, rear part and middle part of the down-scaled forwarder separately.A benefit by doing so is that the IMUs can detect the pitch and roll angle at differ-ent parts of the forwarder since the joint between two parts is not rigid enough toconsider the whole forwarder as a rigid body.

36


Figure 4.2: Genuino 101Current sensor

The current sensor is ACS714 and its wire connection is as shown in Fig. 4.3.ACS714 operates with input voltage +5V which can be powered by the µ-controller.The output voltage is proportional to AC or DC currents with the sensitivity 185mV/A. Six current sensors are required to measure the currents for the six wheels.

Figure 4.3: Current sensorH-bridge

Since the linear actuators require very high power to drive. H-bridge are required todrive the linear actuators. Pololu Dual MC33926 Motor Driver Shield for Arduinois used as shown in Fig. 4.4. The maximum operating voltage is 28V is higher thanthe linear actuator operating range 24V. In addition, there is an Arduino librarymaking it easy to use this motor shield.

Figure 4.4: H-bridge

37


Speed Controller

The EC motor to drive the forwarder is controller by the speed controller ESCONas in Fig. 4.5. A more detailed specification can be referred in the datasheet [37].When programming the controller, some parameters such as motor type, requiredspeed, control method etc. can be deployed by the interface software ESCON Studioas in Fig. 4.6.

Figure 4.5: Speed controller

Figure 4.6: ESCON Studio

4.3 IMU Filter Algorithm Analysis

As mentioned in section 4.2, the built-in IMU on the Genuino 101 board is used.Since the raw data cannot be used directly due to the noises, some filter algorithmshall be designed accordingly. The officially recommended filter algorithm by Ar-duino is Madgwick filter algorithm developed by Sebastian Madgwick [38]. Thealgorithms generate four quaternions from the raw values of a gyroscope and ac-celerometer. The four quaternions are then used to calculate Euler angles pitch,

38


yaw, and roll. The advantages of the algorithm are allegedly computationally inex-pensive and efficient even at low sampling rates.

However, in real practice, it was observed that the dynamic angles obtained fromthe algorithm have a big deviation from the real one by the evidence of a comparisonwith complementary filter [39] as shown in Fig. 4.7.

0 5 10 15 20 25 30 35 40 45

Time (Sec)

-100

-50

0

50

100

150

Measure

d a

ngle

(D

eg)

Complementary

Madgwick

Accurate angle only

when moving slow

for Madgwick filter

Complementary filter functions

well in spite of sudden change

of the angle

Figure 4.7: Filter algorithms comparisonA complementary filter calculates the estimated angle by combining the data fromboth the gyroscope and the accelerometer. An abstract form for complementaryfilter is as in Eq.4.1.

θest = Kgyr × (θest + gyrData× dt) +Kacc × accData (4.1)

where θest denotes estimated estimated angle and Kgyr and Kacc are weight coef-ficients for the angles calculated from gyroscope data gyrData and accelerometerdata accData respectively. From real experience, the coefficients are usually chosenas Kgyr → 1, Kacc → 0 and Kgyr +Kacc = 1.

A detailed explanation is as Fig. 4.8. On the short term, the data from the gyroscopeis used because it is very precise and not susceptible to external forces. On the longterm, the data from the accelerometer is used as it does not drift.

Figure 4.8: Complementary filter principle

39


40

Chapter 5

Results

This chapter presents the results from the simulation as well as the real experiment.For simulation, control effects and comparison of the two control strategies arepresented. For the real experiment, because IMU has problem with the pitch androll measurement, only model verification is given.

5.1 Simulation results

This section show the numerical results from the simulation in terms of tilt anglesand tire pressure.

5.1.1 Tilt Angles

Pitch and roll angle under no control and the two control strategies are shown asFig. 5.1 and Fig. 5.2 respectively. It can be seen that both PID control and on-offcontrol reduce pitch and roll angle errors to a large extent. It seems that on-offcontrol performs better than PID control since it yields a lower pitch and roll peakangle. Also, it is observed that the angle peaks are shifted a bit. it can be explainedby the horizontal movement of the wheels when the linear actuators operate. Inaddition, longitudinal shock can also contribute to the peak shift.

41

CHAPTER 5. RESULTS

Table 5.1: Control effects comparison

Control strategy∫e2pitchdt (deg2 · s)

∫e2rolldt (deg2 · s)

without control 95.25 275.03On-off 18.33 16.15PID 19.45 37.87

0 5 10 15 20 25 30 35

Time (Sec)

-4

-3

-2

-1

0

1

2

3

Pitch (

deg)

Without control

PID control

On-off control

Figure 5.1: Pitch Angle Error

0 5 10 15 20 25 30 35

Time (Sec)

-10

-8

-6

-4

-2

0

2

4

6

8

Roll

(deg)

Without control

PID control

On-off control

Figure 5.2: Roll Angle ErrorA quantitative comparison between PID control and on-off control effects is given inTable 5.1. The evaluation index is chosen as error square integral. PID can reducepitch error up to 79.6% and roll angle up to 86.2%. On-off control can reduce pitchangle up to 80.8% and roll angle up to 94.1%. On-off control outperforms than PIDcontrol on both pitch and roll angle.

42

CHAPTER 5. RESULTS

5.1.2 Tire Pressure

Tire pressure values of different cases are compared in this section. Tire pressurefor each wheel without control, with on-off control and with PID control are shownin Fig. 5.3, 5.4, and 5.5 respectively. It can be observed that there are peaks inthe plots. This could result from numerical errors such as long simulation samplingtime.

43

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

FL

Tire

Pre

ssu

re (

N)

(a) FL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

FR

Tire

Pre

ssu

re(N

)

(b) FR pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

ML

Tire

Pre

ssu

re (

N)

(c) ML pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

MR

Tire

Pre

ssu

re (

N)

(d) MR pressure

Figure 5.3: Tire Pressure without Control

44

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RL

Tire

Pre

ssu

re (

N)

(e) RL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RR

Tire

Pre

ssu

re (

N)

(f) RR pressure

Figure 5.3: Tire Pressure without Control (cont.)

45

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

FL

Tire

Pre

ssu

re (

N)

(a) FL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

FR

Tire

Pre

ssu

re (

N)

(b) FR pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

ML

Tire

Pre

ssu

re (

N)

(c) ML pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

MR

Tire

Pre

ssu

re (

N)

(d) MR pressure

Figure 5.4: Tire Pressure with On-Off Control

46

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RL

Tire

Pre

ssu

re (

N)

(e) RL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RR

Tire

Pre

ssu

re (

N)

(f) RR pressure

Figure 5.4: Tire Pressure with On-Off Control (cont.)

47

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

FL

Tire

Pre

ssu

re (

N)

(a) FL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

FR

Tire

Pre

ssu

re (

N)

(b) FR pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

ML

Tire

Pre

ssu

re (

N)

(c) ML pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

MR

Tire

Pre

ssu

re (

N)

(d) MR pressure

Figure 5.5: Tire Pressure with PID Control

48

CHAPTER 5. RESULTS

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RL

Tire

Pre

ssu

re (

N)

(e) RL pressure

0 5 10 15 20 25 30 35 40

Time (s)

0

100

200

300

400

500

600

700

800

900

1000

RR

Tire

Pre

ssu

re (

N)

(f) RR pressure

Figure 5.5: Tire Pressure with PID Control (cont.)The integral of tire pressure over test time is shown in Table 5.2. There is nodirect evidence showing that the proposed control strategies can reduce tire-terrainpressure. Traction control should be considered to solve this problem.

Table 5.2: Tire Pressure Comparison

∫Ndt (×106Ns) FL FR ML MR RL RR

without control 6.7248 2.2162 3.0045 3.0766 6.5346 8.4980On-off 4.8218 3.9437 6.7591 6.3930 10.286 11.037PID 4.7083 4.1298 7.2176 5.4023 9.5994 12.106

5.2 Model verification

It can be seen in Fig. 5.6 that the forwarder drives under control can behaveaccordingly to some extent. The linear actuator contracted when the wheel is onthe bump. However, during doing real experiment, the forwarder keeps chatteringwhen the linear actuators operate. Because the IMU cannot measure the angle error

49

CHAPTER 5. RESULTS

precisely under dynamic status. The measured data drifts a lot compared with thereal value. Therefore, only the forwarder driving through the test track withoutcontrol are realized. The pitch and roll angle error are then compared with thesimulation value for model verification.

(a) Before the Bump

(b) On the Bump

Figure 5.6: Rear Left Wheel under ControlFig. 5.7 shows pitch angle match degree and Fig. 5.8 shows the roll angle matchdegree. It can be seen that the general trend matches for the both pitch and rollangle. However, when the forwarder drives through the bumps, the IMU measure-ment includes more noise than it is static. In addition, the measured angle becomessmaller gradually. This results from the low rigidity at the forwarder joint whenthe IMU is placed at the front of the forwarder. When the front wheels are on theground and the middle and rear wheels are still going through the bumps, the jointof the forwarder absorbs some of the angle error.

Track position

-5 0 5 10 15 20 25 30 35 40

Pitch a

ngle

(deg)

-6

-5

-4

-3

-2

-1

0

1

2

3

Field test

Simulation

Figure 5.7: Pitch Angle Error Verification

50

CHAPTER 5. RESULTS

Track position

-5 0 5 10 15 20 25 30 35 40

Roll

angle

(degt)

-10

-8

-6

-4

-2

0

2

4

6

8

Field test

Simulation

Figure 5.8: Roll Angle Error Verification

51

CHAPTER 5. RESULTS

52

Chapter 6

Future Work and Recommendations

This chapter presents the troubles faced during the project, the potentials that isworth digging further in the future and the recommendations on this project.

6.1 Faced Troubles

During building simulation model with Simmechanics, some abnormal modelingresults happened occasionally. For example, the intersection between the wheel andthe ground could increase dramatically suddenly. The model run very slow and along sampling period had to be chosen to speed up simulation time. Another methodto reduce simulation time is to decrease the stiffness of the model since high stiffnesswill cause high frequency.

A very challenging part in this project is undoubtedly the hardware implementation.Actually the prototype of the down-scaled forwarder used in the project is sortof fragile. When the chattering problem happened to the forwarder, the wheelsdropped off from the forwarder body. The awkward moment was captured as Fig.6.1. Besides the poor connection between the wheels and the pendulum arms, thejoints of the different parts of the forwarder are also too soft while for the real fullsize forwarder it should be very rigid. The high flexibility of the joints makes themeasured pitch and roll angle different as IMU installation place changes. Whendoing real test, there is one EC motor malfunctioning so there is only total of fivewheels capable of rotating. In addition, since the bumps are made of steel, they arevery slippery. Sometimes the forwarder cannot drive through the bumps and needsome extra push.

53

CHAPTER 6. FUTURE WORK AND RECOMMENDATIONS

Figure 6.1: The Fragile ForwarderThe battery used to actuate the linear actuators and the EC motors drains tooquickly. Normally the battery can only support the experiment for a quite shorttime and then much time is needed to power the battery again. Otherwise the thelinear actuators could not drive the wheels with full speed. This could prevent theconsistency of doing the test.

To determine whether the wheel contacts the ground or not, tyre-ground pressurewas considered to be the index at the first place. To test tyre-ground pressurevalue, off the shelf sensor such as tire-pressure monitoring system (TPMS) wasconsidered useful. However, the sensed value is transmitted in an encrypted way.Therefore current sensor was then chosen as the sensor to tell whether the wheel ison the ground or not. However, in the real test, it was found that when the wheelrotates on the ground, the required current to drive the forwarder is too low to senseaccurately. And the currents in six wheels are very hard to be distributed evenly.An alternative solution to indicate the wheel state should be proposed.

The IMU always has problem with showing accurate angle value. A main reason canbe the selected filter algorithms. As stated earlier, the performance of IMU dependson the filter algorithms greatly. Even though a better algorithm was selected, themeasured signal still includes too much noise. When running Matlab to receive themeasured data from the sensors, it was observed that the data was not received inreal time. So the time scale of the final plot would be different from the real timescale.

6.2 Future Work

Despite of the aforementioned aspects that could be taken care of in the future,there is much space for the new directions of the project. In this thesis work,

54


only pitch and roll angle are considered to be reduced. Other active suspensionevaluation index could be included such as vertical acceleration or angle acceleration.Some comprehensive index such as comfort index can also be considered to evaluatesuspension control performance. Longitudinal shock as mentioned earlier should betreated seriously. The relative angle composed by the pendulum arm and the bumpslope should be employed as control signal for the linear actuators.

Some advanced control strategy should be explored further for the active suspen-sion. A promising method could be compliance control [40]. This might requireto implement force sensors for the linear actuators. Although trying some otheradvanced control strategy, it is inevitable to add new sensors to the forwarder.

55


56

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60

Appendices

Rev. D - Subject to change© Copyright Transmotec

Page 3

www.transmotec.com e-mail: [email protected] USA: +1 339 234 9200Transmotec Phone Europe: +46 8 792 35 30

MODEL NO. DESIGNATIONS

DLA series 50-300 mm 1200 N with potentiometer feedback

ACTUATOR STROKE DATAStroke version B (mm) 50 100 150 200 250 300Retracted length A (mm) 195 246 297 348 399 450Resistance (Kohm) 0.3-9.3 0.3-9.7 0.3-8.6 0.3-9.6 0.3-9.3 0.3-9.3Feedback (ohm/mm) 180 95 55 46 36 30Life time number single strokes 80.000 40.000 26.666 20.000 16.000 13.333Weight (g) 1110 1175 1250 1315 1385 1455

VOLTAGE RATIODLA

Example: DLA-12-5-A-50-POT-IP65

- - - STROKEA- - IP65FEEDBACK -

ACTUATOR DATAReduction 5 10 20 30 40Voltage (VDC) 12/24 12/24 12/24 12/24 12/24Current at max. thrust (A) 3.0/1.5 3.0/1.5 3.0/1.5 3.0/1.5 3.0/1.5Max. thrust (N) 200 300 500 800 1200Static force (N) 1500 1500 1500 1500 1500Speed at max. thrust (mm/s) 35 25 15 10 5

ACTUATOR FEATURES AND STANDARD DATASTANDARD CUSTOMIZATION OPTIONS

Type Electric linear actuatorMotor type Brush PM dc motorCable Flying wire 900 mm YesVoltage 12 or 24 volt dc 36 or 48 volt dcScrew type ACME pitch 3 mmNoise level < 60 db (A) YesLife time 4 million mm total strokeLimit switches Integrated non adjustable Stroke lengthDirection movement By reversing voltage polarity YesStroke tolerance ±3 mm ±2 mmDuty cycle 25%Max. duty operational time 1 min. max. thrustProtection class IP65Insulation class FMax. motor winding temp. 155 ºCEMC EN55014 IEC61000Gear box Metal spur gearsMotor pinion gear Plastic MetalGear box material Zinc alloyRod and house material Aluminum STKM11A Stroke lengthFeedback PotentiometerOperating and storage temperature -26°C~+65°C

Manufacturing quality standards ISO 9001:2008RoHS compliance YesCE label YesUL approval No Yes

POTENTIOMETER FEATURES AND DATAType Wire woundResistance 0.3 - 9.7 KohmResolution 0.025%Resistance tolerance ±5%Linearity ±0.25%

Cable 3+2 leads flying wire 900 mm

Motor

Motor wiring

RED

BLACK

Potentiometer wiring

GND

Output

V input

BLUE

WHITE

YELLOW

CW

82

24

42

Ø20

L=900A ±3 mm

Ø40

36.7

9 Ø812

18

Ø8

Retracted ExtractedB ±3 mm

72

132

20

20

30.5

control strategy investigation for a down- scaled forwarder

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