1. Control and Mobility A1.1 Platform Experimental Study of a MAST Platform in collaboration with Prof. Fearing (Micromechanics Center)

2. Legged robot dynamics are complicated Control and Mobility

3. 1/10 th real-time Legged robot dynamics are complicated Control and Mobility

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

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

6. 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

7. 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

8. 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

9. 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

10. 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

11. Tracking

12. 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

13. Preliminary results Periodic, predictable behavior at low speed

14. Preliminary results SLIP-like height fluctuations at high speed

15. Trajectory Planning Waypoint Navigation with simple hybrid dynamical model –Basic turning techniques known for LLS 1 Execute maneuvers over a variety of terrain types –Robust control achieved via experimental verification 1: Proctor and Holmes, Regular and Chaotic Dynamics 2008