1.49 m step-down

18 cm step-up

Variable Speed Galloping Control using Vertical Impulse Modulation for Quadruped Robots: Application to MIT Cheetah Robot

Hae-Won Park and Sangbae Kim

Dept. of Mechanical Engineering, Massachusetts Institute of Technology

1. Objectives• Present a controller design scheme which provides a robust and variable speed galloping gait on a quadruped robot.

• Handle variable speed from slow (~3 m/sec) to fast (~15 m/sec) as well as unexpected variations in ground height.

• Respect constraints on actuator saturation and ground reaction forces.

3. Our Approach

• Ground Reaction Force (GRF) Profiles[1][2]

1) Insights from biology 3) Convert to a State Feedback

• Constant swing time for a wide range

of the speed[3]

• Swing leg retraction

Swing

Stance

Speed (m/sec)

Tim

e (

Sec)

2) Limit Cycle Design

• Ground Reaction Force Profiles

60

0

-60GRFx

(N)

350

200

0GRFy

(N)

• Gait Pattern

Swing Leg

Retraction• Constrained Optimization

- EQ: Periodicity condition

- INEQ: Satisfy a friction cone, bounded body

oscillations, and avoid leg collapsing

Minimum of Cmt , slip distance, and peak

transverse force occurs with a near-zero

foot tangential speed[4].

GRF profiles Virtual spring

and damper

Slip avoidance

2. Control Design Principles• Take insights from biology, find a limit cycle, and convert to a state-based control consisting of four phases.

• Manage transitions between phases using a simple state machine.

• Gait Pattern Stabilizer

• State Machine

• Speed Control via Impulse Modulation

Slow Speed Fast Speed

Scale

4. Results1) Speed Control

• 3 m/s ~ 14.9 m/s

(30 Nm torque)

• Slow speed:

Anti-Horse-like Gallop

• High speed:

Cheetah-like Gallop

2) Robustness Test

• Single Step disturbance

• Randomly Varying Ground

5. Extensions• Obtain trot gait by modifying gait pattern

• Transition between Trotting and Galloping

by smoothly changing gait pattern

• Robust 3D trotting and galloping

(recovery from 150 N sideways push)

6. References

[1] Walter et al. (2007) J. of Exp. Biol.

[2] Hudson et al. (2012) J. of Exp. Biol.

[3] Maes et al. (2008) J. of Exp. Biol.

[4] Haberland et al. (2011) IROS

[5] Bertram et al. (2009) J. R. Soc.

- 80 steps trial on rough ground.

- 95% success rate for ground height

variation of σ = 17.6 cm Click for video Click for video

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