larm clutched arm 2011 m bdsm

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Mechanics Based Design of Structures and Machines: An

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A Multiobjective Optimal Path Planning for a 1-DOFClutched ARMHao Gu

a& Marco Ceccarelli

a

aLaboratory of Robotics and Mechatronics (LARM), Department of Mechanics, Structures,

Environment and Territory (DIMSAT), University of Cassino, Cassino, Italy

Available online: 10 Jan 2012

To cite this article: Hao Gu & Marco Ceccarelli (2012): A Multiobjective Optimal Path Planning for a 1-DOF Clutched ARM,Mechanics Based Design of Structures and Machines: An International Journal, 40:1, 109-121

To link to this article: http://dx.doi.org/10.1080/15397734.2011.609090

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Mechanics Based Design of Structures and Machines, 40: 109121, 2012

Copyright Taylor & Francis Group, LLC

ISSN: 1539-7734 print/1539-7742 online

DOI: 10.1080/15397734.2011.609090

Innovative Application Brief

A MULTIOBJECTIVE OPTIMAL PATH PLANNINGFOR A 1-DOF CLUTCHED ARM#

Hao Gu and Marco Ceccarelli

Laboratory of Robotics and Mechatronics (LARM), Department of Mechanics,

Structures, Environment and Territory (DIMSAT), University of Cassino,

Cassino, Italy

In this paper, a procedure of optimal path planning is proposed for the operation of the

anthropomorphic low-cost easy-operation LARM clutched arm with only one actuator.

An algorithm is proposed for path planning of the arm motion with multiobjective

considerations that take into account of traveling time, energy consumption, and end-

effector performance. Numerical examples and laboratory experiments are reported to

show the feasibility of the proposed path planning and the efficiency of the LARM

clutched arm.

Keywords: Clutch systems; Humanoid robots; Robotic arms; Path planning.

INTRODUCTION

Industrial robots are typical examples of robotic arms, which are widelyused in factory today (ABB, 2011; COMAU, 2011; KUKA, 2011). Other popularexamples are the robotic arms in humanoid robots like in ASIMO by Honda (2011),and ARMAR by University of Karlsrahe (Albers et al., 2007), and the Care-O-bot by Fraunhofer IPA (Graf et al., 2009). Most of these existing robotic arms aredesigned as multiactuator systems, which operate with fast movement and precisepositioning. But they are very expensive and complex systems for no expert users.

Mainly for service applications in home and public places, very precise ordexterous manipulations are not, in general, required (Morales et al., 2005). Thus,

it is possible to design a robotic arm simpler and cheaper, by reducing the numberof actuators, as attempted in Nakamura et al. (2001), Karbasi et al. (2006), andGu et al. (2010). However, the nonholonomic solution in Nakamura et al. (2001)increases the control complexity; the Chebychev-Pantograph mechanism in Nava(2006) does not provide a sufficient workspace; the Unidrive Modular Robot systemin Karbasi et al. (2006) is not suitable for robotic arms; and the Armatron (Carroll,

Received April 5, 2011; Accepted July 11, 2011# Communicated by P. Larochelle.Correspondence: Hao Gu, Laboratory of Robotics and Mechatronics (LARM), Department

of Mechanics, Structures, Environment and Territory (DIMSAT), University of Cassino, Via G. DiBiasio, 43, Cassino 03043, Italy; E-mail: [email protected]

109


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110 GU AND CECCARELLI

2007) is just a toy with no automation built in and no proper payload capability forpractical applications.

At LARM (Laboratory of Robotics and Mechatronics, University of Cassino,Italy), a new robotic arm named as LARM clutched arm (Gu et al., 2010) has been

proposed with only a single motor by using a clutch system. Such a 1-DOF solutionis still versatile within a 3D workspace. In previous works (Gu et al., 2010; Gu andCeccarelli, 2010a), simulations and preliminary experimental tests have validated thefeasibility of the design concept. Recently, a prototype has been built with a propercontrol system.

The operation task for LARM clutched arm can be summarized as in twoparts: trajectory planning, in which the arm generates a prescribed trajectory, andoptimal path planning, in which a point-to-point motion is optimized to achievecertain task objectives. The trajectory-planning task has already been achieved withan efficient algorithm in Gu and Ceccarelli (2010a). Optimal path planning can

strongly affect the efficiency of using its single actuator. Moreover, a proper pathcan particularly overcome its natural drawback in terms of operation speed.A preliminary study on an optimal path-planning task has been carried out

by investigating the planar motion of the limb part in a 2D optimal path planningin Gu and Ceccarelli (2010b). However, the multiobjective formulation in Guand Ceccarelli (2010b) is not completely formulated to evaluate the path-planningcharacteristics, and the numerical results in Gu and Ceccarelli (2010b) are notvalidated by tests.

The purpose of this paper is to present a proper procedure of optimalpath planning for such a new robotic arm with 1-DOF by using numerical andexperimental results to show its engineering feasibility.

THE LARM CLUTCHED ARM

The conceptual design of the LARM clutched arm consists of a compactshoulder that can perform required rotations (R1 to R3) for a three-revolutemanipulator. The main idea is to use a proper clutch system to obtain threesubmotions from the source motion of a single motor.

Figure 1 illustrates the mechanical design of the shoulder, which is the key partto achieve the concept idea into a practical system. This shoulder-centered designmakes the main mass of LARM clutched arm concentrated on the arm fixed frame,and the limb part can be lightweight.

In the scheme of Fig. 1(a), symbols Gia/b i = 16 and Bia/b i = 1 2represent gears and belt wheels, respectively, Wia and Wib i = 1 2 representthe worm and the worm wheel, respectively. Electromagnetic clutches named asCi i = 13 are assembled along rotating axes. By changing the states of clutches,the gearing system can be activated in 23 = 8 modes. The self-locking feature ofworm and worm wheel eliminates the need of braking power. Possible operationmodes (OP) for LARM clutched arm are listed in Table 1, where 0 means that aclutch is deactivated and 1 a clutch is activated. In particular, OP0 is a stationarymode, with null energy consumption.

A built prototype of LARM clutched arm is illustrated in Fig. 2. It has

dimensions more or less like a human arm, with 3-kg weight and 2-kg payloadcapability.


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PATH PLANNING FOR A 1-DOF CLUTCHED ARM 111

Figure 1 The LARM clutch system in the shoulder design: (a) a scheme; (b) a CAD design.

Table 1 The operation modes for LARM clutched arm (Gu and Ceccarelli, 2010a)

Operation mode OP0 OP1 OP2 OP3 OP4 OP5 OP6 OP7

Active rotations None R1 R2 R3 R1 & R2 R1 & R3 R2 & R3 R1R3

C1 0 1 0 0 1 1 0 1C2 0 0 1 0 1 0 1 1C3 0 0 0 1 0 1 1 1

A proposed controller for LARM clutched arm consists of a servo amplifierfor DC motor, a Programmable Logic Controller (PLC) for electromagneticclutches, and a National Instruments (NI) Peripheral Component Interconnect(PCI) board for communications. The whole system (except PC) requires only acommon 24V DC power supply, which can be an advantage for applying it on

Figure 2 A prototype of LARM clutched arm (Gu and Ceccarelli, 2010a): (a) the overall structurewith the control system; (b) the clutch system in the shoulder.


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mobile robots with a commercial battery. A Graphic User Interface (GUI) has beenprogrammed with LabVIEW, which can control and monitor the arms motionthrough suitable virtual instruments.

Summarizing, LARM clutched arm has the following novel characteristics:

- lightweight limb design, with low-cost, low energy consumption, and easyoperation;

- 1-DOF clutched solution with motion capability in a 3D space;- avoiding overheat of motor, since the motor works only for actuating the arm and

self-locking mechanisms ensure the arm to maintain its posture once the arm isstationary.

OPERATION CHARACTERISTICS OF LARM CLUTCHED ARM

Operation modes OP1OP7 can be expressed as vectors in the joint spaceand combined modes like OP4, OP5, OP6, and OP7 have a constant slope that isdetermined by the reduction ratios in the mechanical design. Thus, it is convenientto search the optimal path in the joint space.

In Fig. 3(a), a typical prescribed task can be given by the start and end pointswith several path possibilities given by OP vectors in joint space. For example, thedashed line in Fig. 3(a) indicates a path that is composed of two segments (SG1,SG2) by means of OP3 and OP2, respectively. Another path is indicated by a solidline, which has three segments (SG1SG3) with OP2, OP6, and OP3, respectively.

A path segment SGi i = 1N contains two kind of information, namely, adiscrete one for the selected operation mode (OP) and a continuous one for the

motor displacement D. Therefore, a path can be characterized by a sequence ofsegments with data for OP and D. For example, the segment sequence in Fig. 3(a)is given as OP2, OP6, and OP3 with D1, D2, and D3, respectively, and can be usedas a command sequence for the path planner in the controller.

Figure 3 An example of the operation for LARM clutched arm: (a) path possibilities in joint space;(b) a controlled path generation with the proposed strategy.


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Figure 3(b) illustrates the proposed control strategy to coordinate the motor

and operation mode for the solid path in Fig. 3(a). The motor is controlled with

a smooth speed to output a desired angular displacement for each segment (SG1

SG3) while clutches only change their states when the motor stops. The transient

dynamics caused by clutch actions can be strongly limited and even avoided with

suitable delay time tS for motor activation, as indicated in Fig. 3(b). For the

prototype, a tS delay of 80msec has been experienced as suitable enough.

Thus, an optimal path-planning task is to seek a proper sequence of segments

with certain operation modes and motor displacements as variables of the path-

planning problem.

For traditional robotic arms, the actuator for each DOF is independent and

in a point-to-point optimal path planning, the main effort is to optimize the motion

of each actuator (Ceccarelli, 2004). For the LARM clutched arm with 1-DOF, the

single actuator is shared by three joints, which are dependent to each other whenthey are activated simultaneously. The optimal path planning for LARM clutched

arm concentrates on a proper sequence of OP. The single actuator only serves

the robotic arm to implement the selected OP actions with suitable cooperation to

clutches.

In the block diagram of Fig. 4, the optimal path planning for LARM clutched

arm depends of the three variables OP, D, and N, and outputs command sequences

of OP and D. The controller can interpret such command sequences into control

signals for motor and clutches with a proposed control strategy as in the example

in Fig. 3(b). With a feedback of speed, the motor is controlled to track the desired

smooth motion with a proper PID law.A cubic function can be chosen for the desired motor speed, in order to

achieve smooth and differentiable features. The motor displacement command in

kth segment is Dk. A symmetrical speed up and down motion lasts for tk with a

speed peak of Pk. Since the area enveloped by the speed curve is the displacement,

Figure 4 A schematic diagram for the control of LARM clutched arm.


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Dk, tk, and Pk are linked by the relationship

Dk =tk2

Pk (1)

The mean acceleration aM for speeding up to Pk can be given by theexpression

Pk =tk2

tg =tk2

aM (2)

If the value of aM is given, substituting Equation (2) into Equation (1), tk canbe obtained as

tk = 2Dk/aM (3)Thus, Pk can be fixed by substituting Equation (3) into Equation (2).

Consequently, Pk and tk can be expressed as monadic functions of Dk. For theprototype, an aM of 2000 deg/sec

2 has been experienced as a suitable value.In addition, the motor has a limited speed with Pmax, and a large Dk may cause

Pk to exceed Pmax. In this case, Pk and tk should be recomputed with the conditions

Pk = Pmax(4)

tk =2DkPk

Once Pk and tk are determined, the cubic speed can be formulated byidentifying coefficients in

motor =

b2t

2 + b3t3 t 0 tk/2

Pk b2t tk/22 b3t tk/2

3 t tk/2 tk(5)

with b2 = 12Pk/t2k and b3 = 16Pk/t

3k.

Considering the delay tS, the motion period Tk for kth segment is expressed as

Tk = tS + tk (6)

Equations (1)(6) summarize the motion generation process for the motor,which is executed by the controller when it reads a command Dk in kth segment.

A FORMULATION FOR OPTIMAL PATH PLANNING

An operation with low energy consumption and smooth behavior can beobtained by using basic criteria for an optimal path planning.

Time is an important issue when a robot serves a human although theaction of anthropomorphic robotic arm is not expected to be as fast as industrial

manipulators. Although the mechanical design of LARM clutched arm gifts energysaving features, how to use the single motor and clutches properly and efficiently


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is still a question for low energy consumption. Accelerations of the end effectorcan directly indicate the motion characteristics. For friendly and safe purposes, theacceleration aH should be minimized during a task of LARM clutched arm.

Thus, an optimal path planning of LARM clutched arm can be formulated

as a multiobjective optimization problem with traveling time Ttra, consumed energyEcon, and maximum acceleration aH of the end effector in the form

min f = f

TtraTref

EconEref

aHaref

(7)

subject to

1 1min 1max

2 2min 2max

(8)E Emin Emax

motor Pmax Pmax

where Tref, Eref, and aref are reference values and 13 are the joint angles withE = 3 2 as the elbow angle.

By using weighting sum strategy (The Math Works, 1992), the multiobjectiveproblem in Equation (7) can be converted into a scalar one in the form

min f = w1TtraT

ref

+ w2EconE

ref

+ w3aHa

ref

(9)

in which w1w3 are weighting factors with condition 0 wi 1 i = 13 and w1 +w2 + w3 = 1.

Since the three criteria in Equation (9) can be competitive to each other, aweighting factor of the most emphasized criterion can be conveniently consideredas for major effect.

For a path with N segments, the traveling time can be computed as sum oftime segments with Equation (6). The consumed energy Econ can be computed bysumming the work of the motor Wmotor and the work of electromagnetic clutchesWclutch. Wmotor can be computed as

Wmotor =N

k=1

Tk0

motormotordt

(10)

where motor is the actuating motor torque. Since the power of the selectedelectromagnetic clutch in the prototype is given as Pwclutch = 72 W, Wclutch can becomputed as

Wclutch =N

k=1nOPTkPwclutch (11)

in which nOP is the number of activated clutches depending on the OP mode.


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Figure 5 A kinematic model of the LARM clutched arm (Gu and Ceccarelli, 2010a).

Acceleration aH can be computed by referring to Cartesian Space coordinates(x, y, z) in the form

aH = Max

x2 + y2 + z2 (12)

Since the LARM clutched arm can achieve any point-to-point task (within itsworkspace) with OP1, OP2, and OP3 sequentially, a reference operation mode can

be defined with utmost those three segments to compute Tref, Eref, and aref.The computation of Wmotor and aH requires evaluation of the arms kinematics

and dynamics. LARM clutched arm can be considered as a two-link planarmanipulator rotating around the Y-axis with dimensions L1, L2, and L3 (L0 isshoulder size in a trunk body; Fig. 5). The rotating plane for upper arm and forearmis defined as S-plane with coordinate XsYs. The Forward Kinematic Problem (FKP)and Inverse Kinematic Problem (IKP) of LARM clutched arm can be expressed byusing the model in Fig. 5.

The dynamics of a model with concentrated link masses can be computed togive the motor torque motor as

motor = C11/K1 + C22/K2 + C33/K3 + f (13)

in which K1, K2, and K3 are reduction ratios for three gear trains; Ci i = 13indicates the clutch state that equals to 1 or 0; i i = 13 is the output torquefor each joint. It means that when clutch Ci is deactivated, the link output torque ido not require motor torque, since the self-locking mechanism ensures the brakingaction. f is a torque considering friction and other secondary effects that aregenerated in the gear trains. Since it is difficult to formulate accurately a f as inpractical case, it has been convenient to identify f approximately via tests on the

prototype, in which f considers all the dissipative effects as computed by comparinga numerical result with an experimental test. With a payload of 0.25kg on the arm


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extremity, f has been measured from 0.167Nm up to 0.271Nm as depending onthe operation mode, with the maximum value when all gear trains are activated.

A NUMERICAL PROCEDURE FOR OPTIMAL PATH PLANNING

Since path generation for LARM clutched arm with OP vectors can beconsidered as a 3D robot navigation procedure in joint space, widely used ArtificialIntelligence (AI) methods in the optimal path planning can be also properly applied.

Among many approaches in AI area, A* (A star) is one of the most commonand well-known heuristic graph-searching algorithm (Nilsson, 1982). In order touse A*, a node structure can be defined with information on path-planningcharacteristics that are related to f objective function in Equation (9). Parameterh is the predict estimate to reach the goal end point, which provides the heuristic

information for the A* search (Nilsson, 1982), as the distance left to the goal withthe expression

h =

1 1end

2 + 2 2end2 + 3 3end

21start 1end

2 + 2start 2end2 + 3start 3end

2 (14)

in which (1start, 2start, 3start) and (1end, 2end, 3end) are joint coordinates for startpoint and end point, respectively. The cost for a node is a sum of f and h. A nodewith minimal cost will be selected firstly in the path search.

Figure 6(a) illustrates a node expanding process with OPs, where a father nodeis a current selected node while son nodes are those expanded from the father node.The depth information of a node increases by 1, which can indicate the order ofgeneration for the node. In Fig. 6(b), a more visual scheme for node expansion isindicated in joint space, where black circles are for father nodes, and white circlesare for son nodes.

One important issue is that each node will remember its father node andpointers of the son nodes will point to the data address of their father node. In sucha way, once a node is on the goal, the optimal path can be obtained by trackingback with pointers.

Figure 6 A scheme for node expansion: (a) in the node tree; (b) in the joint space.


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When a motion step of motor motor is given, the joint coordinates of thenew expanded nodes can be updated with expressions as

i = i + Cisign OP /Ki i = 1 3 (15)

where OP can be either positive or negative for forward or backward movement.

NUMERICAL EXAMPLE AND TEST RESULTS

A numerical example is reported as referring to the case with weighting factorsfor Ttra, Econ, and aH with decreasing values w1 = 06, w2 = 03, and w3 = 01,respectively. A start point in joint space is given as (90, 90, 0), while an endpoint is given as (130, 60, 40). motor is given at 100

. Joints ranges are setwithin the arm workspace.

The reference operation with the sequence OP1, OP2, and OP3 is used tocompute Ttra, Econ, and aH as Tref, Eref, and aref for the optimal solution. Results forthe optimal path that is obtained with the sequence OP3, OP4, OP1 are reportedin Figs. 79.

The computed traveling time with 5.63sec is shorter than in the referenceoperation with 7.24sec; the corresponding values for D1, D2, and D3 are 3000,2300, and 200; the energy consumption is 73.30J and acceleration is 0.28 (m/sec2)much smaller than in the reference operation. The cost function converges to a valueof 0.90 from the initial value of 1.00 after only 172 iterations. Initial values of f andh are 0 and 1, respectively, since in the start point Ttra, Econ, and aH are zeros while

the predicted estimate to the end point is full. When the robotic arm reaches the endpoint, f and h converges to 0.89, and 0.01, respectively. With an average consumingpower at about 13W (Econ/Ttra) and a maximum end-effector acceleration at no

Figure 7 Computed optimal path: (a) in joint space; (b) in Cartesian space (solid line is for optimalpath and dashed line is for reference path).


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Figure 8 Experimental result of time evolution for motor speed and torque in the optimal operation(solid line is for optimal operation and dashed line is for reference operation).

more than 03 m/sec2, the optimal operation can still be considered as energy savingand gentle behaved.

Experimental tests have been carried out on the prototype with the optimalpath operation whose results are reported in Figs. 8 and 9. Due to the self-locking gearing systems, the motor torque returns to zero when the operationtask finishes. In Fig. 9, test results of the consumed energy for optimal andreference operation give 75.13 and 68.73 J, respectively. They are close to thenumerical results. In addition, Econ in the test for the optimal operation increaseswith respect to the reference operation, as happened in the numerical case too. Inorder to have a further comparison, numerical time evolution of Econ for optimaloperation has been added in Fig. 9 as a dot-dashed line. It can be observed that

Figure 9 Experimental result of time evolution for energy consumption in the optimal operation (solid

line is for optimal operation, dashed line is for reference operation, and dot-dashed line is for optimaloperation in numerical computation).


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test result fits the numerical one with a similar trend shape. Due to the backlashand insufficient stiffness effects in the first prototype of LARM clutched arm,end-effector accelerations in the test are not exactly the same as the numerical ones.

CONCLUSIONS

A novel clutched robotic arm with only one motor has been describedas suitable for anthropomorphic operations. A multiobjective formulation hasbeen proposed for path planning with a comprehensive consideration of travelingtime, energy consumption, and end-effector behavior. A numerical procedure hasbeen presented by using an AI algorithm with computationally efficient features.Numerical examples and test results have shown the engineering feasibility of theproposed procedure of optimal path planning for 1-DOF LARM clutched arm withfast movement, low energy consumption, and gentle behaviors.

ACKNOWLEDGMENT

The first author would like to acknowledge China Scholarship Council (CSC)for supporting his PhD study and research at LARM in the University of Cassino,Italy, for the years 20082010.

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larm clutched arm 2011 m bdsm

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