C4: Project Formulation

1. C4: Project Formulation ESE 313 February 29, 2011 Adam Komoroski Carol Wong

2. Overview Problem Statement: 1. Desired Behavior: 2. Present Unavailability: 3. Desirability of Bio-inspiration: The Hypothesis 4. The Idea 5. Refutability 6. Necessary Means

3. C.1 : Desired Capability • Observed Problem: complete loss of one leg function • Observed Result: unpredicted and uncontrollable motions • Desired Behavior: fault tolerance; directed, controlled, and purposeful movement. • Ability to compensate for the complete loss of function in one leg, restoring motion to a state comparable to full legged functions. • Bio-inspiration: • Variations in leg load bearing • Rat motor cortex injuries • Neural plasticity

4. C.2 Present Unavailability "The problem of fault recovery represents a vast, important domain in its own right that is still relatively unexplored in robotics.” [2] • Much research done on fault-tolerable gaits in the specific instance of locked joint failure • Does not apply to Junior’s locomotive system • Ideas can be extrapolated

5. C.3 Desirability of Bio-inspiration • Mathematical models available • Biological observations that are relevant made • Rats with motor cortex injuries: • Solid observations made that can be extrapolated to Junior platform • Plasticity :Animal analogs have uncanny ability to adapt to injuries and other sustained handicaps • Load Bearing • Remaining questions: • How do we implement an artificial rendering of neural plasticity?

6. C.4 The Idea • Current implementation: http://kodlab.seas.upenn.edu/Aaron/Iros10, :43 • Five legged “crawl” • All five legs offset from each other • Upper left leg (0) loss of function • 3,1,5,2,4 • Four Buehler clock parameters same across all 5 legs • Transition to stable gait • Proposed implementation: • Focus: purposeful disabling of one corner leg • Goal: transition effectively, stabilize resulting crawl gait • Optimize velocity of five legged gait • Stabilizing transition • Mathematical approach: optimize parameters via Nelder -Mead and machine learning algorithms • Bio-inspired approach: vary load bearings on select legs

7. C.5 Refutability • Evaluation of Performance: • Stable gait: readings of IMU, acceleration, center of mass changes • Efficient: energy expenditure • Directed gait: ability to transverse pre-designated path; observation • Controlled gait: velocity controlled and optimized; velocity tracker

8. C.6 Necessary Means • Proposition: • Bioinspired approach: • Determine parameters that change load bearing on a given leg • Purposefully influence load bearing characteristics on legs • Evaluate performance • Mathematical model approach: • Nelder Mead Algorithm: optimization of ‘objective function’ • Objective function: characterizes system parameters and behavior • Machine learning classifiers • Collect data -> observe behavior -> formulate model -> model = objective function

9. QUESTIONS?

10. Five Legged “Crawl” Gait

11. Nelder Mead Algorithm