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) Time (Sec) 2) Limit Cycle Design • Ground Reaction Force Profiles 60 0 -60 GRFx (N) 350 200 0 GRFy (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 C mt , 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. Results 1) 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 Click for video Click for video Click for video Click for video Click for video Click for Video O verview