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