Control and MobilityA1.1 Platform

Experimental Study of a MAST Platform

in collaboration with Prof. Fearing (Micromechanics Center)

Legged robot dynamics are complicated

Control and Mobility

1/10th real-time

Legged robot dynamics are complicated

Control and Mobility

Experiment Setup

• Robot experiments are filmed simultaneously by three consumer-grade high-speed video cameras (Casio Exilim FX-1).

Camera Calibration

• Three high-speed video cameras view calibration object– Casio Exilim FX-1, 384x512 px @ 500 fps

Camera Calibration

• Three high-speed video cameras view calibration object– Casio Exilim FX-1, 384x512 px @ 500 fps

• Find marker locations in video, construct direct linear transformation (DLT)1 T between Cartesian coordinates and video pixels:

1: Hedrick, Biomechanics & Biomimetics 2008

Backpack Calibration

• Affix backpack with known marker locations to robot chassis– Manufactured using 3D printer

• Associate 3D marker locations with markers in video through DLT– Image segmentation using MATLAB

Backpack Tracking

• Estimate SE(3) state (x,y,z,roll,pitch,yaw) using Unscented Kalman Filter (UKF)1

– DLT provides observation function between Cartesian coordinates and video pixels

• UKF provides better estimates for nonlinear systems than Kalman Filter or Extended Kalman Filter

1: Julier and Uhlmann, Proc. SPIE 1997

Foot Tracking

• Measure foot trajectories– Determine contact time, relative phase

• Compare with predicted kinematics– Estimate manifold traversed by feet

• Foot trajectories give basic insight into effect of different terrain types

Motor Speed Measurement

• Measure back-EMF from DC motor– Well-characterized relationship to

motor speed

• Sync motor data stream with videos using flashing LED on robot– Transmit motor data over Bluetooth to

laptop

• Motor speed currently the only input– Control authority extremely limited

Tracking

Hybrid Dynamical Modeling

• Project SE(3) trajectories onto longitudinal and horizontal planes, compare with existing models for legged runners– Fit models to data using hybrid system identification

• Spring-Loaded Inverted Pendulum– Longitudinal-plane running– Holmes et al, SIAM Review 2006

• Lateral Leg-Spring (LLS)– Horizontal-plane stability and turning– Holmes et al, Biological Cybernetics 2004

Preliminary results

• Periodic, predictable behavior at low speed

Preliminary results

• SLIP-like height fluctuations at high speed

Trajectory Planning

• Waypoint Navigation with simple hybrid dynamical model– Basic turning techniques known for LLS1

• Execute maneuvers over a variety of terrain types– Robust control achieved via

experimental verification

1: Proctor and Holmes, Regular and Chaotic Dynamics 2008