compliance in robot legs
DESCRIPTION
Compliance in Robot Legs. Jonathan Hurst. Outline. Introduction What is the long-term goal of this work? What is the intent of this presentation? Background, motivation Running: Spring Loaded Inverted Pendulum (SLIP) Why are real springs important? Future work Current Research Hardware! - PowerPoint PPT PresentationTRANSCRIPT
Compliance in Robot Legs
Jonathan Hurst
Outline Introduction
What is the long-term goal of this work? What is the intent of this presentation?
Background, motivation Running: Spring Loaded Inverted Pendulum (SLIP) Why are real springs important? Future work
Current Research Hardware! Simulation and Control (in collaboration with Joel Chestnutt) Future work
Introduction
The long-term goal is to build a bipedal robot that can walk, run, jump, hop on one foot up stairs, recover from a stumble, and generally behave in a dynamically stable manner
The goal of this presentation is to convince the listener of the following: Series compliance is essential for a successful running
robot Physically varying the stiffness of this series compliance is
useful
Running Animals
Compliant elements in limbs, used for energy storage
Energy consumption is lower than work output
The motion of the center of mass of a running animal is similar to that of a pogo stick, and is common to all animals [Blickhan and Full, 93]
Running Running is loosely defined
Aerial phase Energy transfer
The Spring Loaded Inverted Pendulum (SLIP) model [Schwind and Koditschek, 97] closely approximates the motion of a running animal’s center of mass Assumes no leg dynamics at all
during flight Assumes lossless, steady state,
cyclical running gait Assumes point mass ballistic
dynamics for mass
Ideal, lossless model
SLIP Control inputs:
Leg Touchdown Angle, Leg Stiffness, K Spring rest position, X
Gait parameters at steady state [schwind, kod, 97]: Leg + Ground Stiffness Leg Length at the bottom of
stance phase Leg angular velocity at the
bottom of stance OR
Stride Length Hopping Height Leg + Ground Stiffness
SLIP: Observations of Animals Animals maintain a relatively constant stride length,
and change leg stiffness for these reasons: Changing ground stiffness Different speeds within a gait Changing gravity or payload
Ground stiffness changes are a bigger problem for bigger animals[Ferris and Farley, 97]
SLIP: stiffness adjustment vs. mass From experimental
observations, leg stiffness scales with animal body mass[Farley, Glasheen, McMahon, 93]:
Springs in series add as inverses:
Ground stiffness changes significantly for different terrain types
The lower the leg stiffness, the less global stiffness is affected by changing ground stiffness
SLIP:
Observations of animal behavior gives us hints, not proofs
Do we really need a physical spring, or is spring-like behavior achievable without one? Springs are needed for energetic reasons Springs are needed for power output reasons Springs are needed for bandwidth reasons
Energetics Energy consumption should be
minimized when designing and building a running robot Tether-free Large payload capacity Long battery life
Natural dynamics affect energy consumption
Mimicking the control model (SLIP) with the system’s natural dynamics is a good idea. So far, every running robot has used physical series springs.
Energetics: CMU Bowleg 70% spring restitution Mass distribution:
0.8% spring 5% batteries 20% entire mechanism 80% ballast
Used a spring hanging from the ceiling to simulate operation in 0.35G
Tensioned leg spring during flight If a slightly larger motor replaced
some ballast weight, the Bowleg could hop in 1G, but not without the spring
Energetics: ARL Monopod
The most energy-efficient legged robot
Running speed of 4.5 km/h Total power expenditure of
48W 10.5 Joules of energy
exerted by leg motor in each hop, for 135J of mechanical work
Energetics A 4kg robot hopping 0.5m high yields a flight
phase of 0.632 seconds Assume stance and flight are symmetrical:
Constant force of 40N Work output of 20J Power output of 32W
Robot with series spring and 70% restitution: Constant force of 40N Work output of 6J by the motor, 14J by the
spring Power output of 3.8W by the motor, 28.8W by
the spring Violating the assumption of constant force
spring only enhances the difference, favoring the series-spring method
Power Considerations
Bandwidth Considerations Reflected rotor inertia dominates the natural
dynamics
Inertia is proportional to the square of the gear reduction
Given the following values: Gear reduction = 16 rev/m Rotor inertia = 0.00134 kg-m2
Reflected inertia of the motor is equivalent to leg mass of 13.5 kg
Kinetic energy in leg momentum is lost as an inelastic collision with the ground (a high-frequency input)
For a 30kg robot, much of the energy will be lost in an inelastic collision, and cannot be recovered through the electric motor
Summary of the facts so far: Animals have leg compliance SLIP
Stride Length Hopping Height Leg + Ground Stiffness
Animals physically vary leg stiffness
Series springs are important: Bandwidth Power Energy
Further Research
I think variable stiffness is important for a human-scale legged robot
The extent to which physically variable stiffness is important should be calculable
•Can’t make the stride length longer
•Can’t lower hopping height
•Stiffness is the only thing left!
Current Research
Actuator with physically variable compliance 2-DOF device, 1-DOF actuator
Motor 1: spring set point Motor 2: cable tension=spring stiffness
Mechanism Design Cable drive Lightweight – about 3 kg Fiberglass springs for high
energy density Spiral pulleys impart
nonlinearity to spring function
Electric motors allow for precise control
Very low friction on the “leg” side of the springs
Mechanical Model
time
time
Motor P
ositionLeg P
osition
Control
Control
Performance We created a plot of
comparative max forceagainst frequency.
Peak spring force is measured on two models: The dynamic simulation, with physically
realistic spring adjustment limits and the controller on M1
An idealized simulation, with no spring adjustment limits and M1 held stationary
X2 is forced to a sine function, cycling from 1 to 100 Hz
If the Bode plot for the dynamic simulation were divided by the Bode plot for the idealized simulation, this would be the result.
Frequency-Magnitude plots
Frequency-Magnitude Plots
Physical adjustment is limited to 10 kN/m
Two discrepancies are apparent: 0.78 is the difference between
f=kx, described by the software controller, and the polynomial fit of our physical spring function
0.6 is the difference between the peak forces of the natural dynamics of the two systems
System validation
We built a simulation of a runner with the full dynamic model of the actuator built in – so it’s almost a SLIP
Raibert-style controller commands leg angle, energy insertion for a SLIP
Future Work
Show analytically how bandwidth is affected by the various parameters and situations of the actuator
Calculate the required range of variable stiffness, and rate of change
Put a hip on this thing, make it hop Research and implement controllers for hopping
height, stride length, speed on a step-to-step basis Working with a team, build and control a running
biped that can hop on one foot up stairs