Compliance in Robot Legs

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Compliance in Robot Legs

• Jonathan Hurst

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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

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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

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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

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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 animals 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
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SLIP

• Control inputs
• Leg Touchdown Angle, q
• 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

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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 animalsFerris and Farley, 97

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SLIP stiffness adjustment vs. mass

• From experimental observations, leg stiffness
  scales with animal body massFarley, 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

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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

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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
  systems natural dynamics is a good idea. So
  far, every running robot has used physical series
  springs.

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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

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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

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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

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Power Considerations
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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

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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

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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

• Cant make the stride length longer
• Cant lower hopping height
• Stiffness is the only thing left!

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Current Research

• Actuator with physically variable compliance
• 2-DOF device, 1-DOF actuator
• Motor 1 spring set point
• Motor 2 cable tensionspring stiffness

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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

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Mechanical Model
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Motor Position
time
Leg Position
time
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Control
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Control
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Performance

• We created a plot of
• comparative max force
• against 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.

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Frequency-Magnitude plots
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Frequency-Magnitude Plots

• Physical adjustment is limited to 10 kN/m
• Two discrepancies are apparent
• 0.78 is the difference between fkx, 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

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System validation

• We built a simulation of a runner with the full
  dynamic model of the actuator built in so its
  almost a SLIP
• Raibert-style controller commands leg angle,
  energy insertion for a SLIP

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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

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