Generation and Testing of Gait Patterns for Walking Machines Using Multi-Objective Optimization and Learning Automata Jeeves Lopes dos Santos Cairo L. Nascimento Jr. Instituto Tecnológico de Aeronáutica São José dos Campos - Brazil

Motivation To develop machines with greater mobility and intelligence that can act as human helpers (dirty, dull or dangerous jobs), our modern era slaves. To develop a gait generation algorithm for walking machines with different morphologies without having to describe mathematically their dynamic models. The proposed gait should be defined considering: the machine’s frontal speed, the smoothness of the robot CG movements, the torques applied to each joint, the total energy consumed for locomotion. 2/10 2

Coordination Strategy Adopted Strategy Coordination Strategy Real Robot Simulated Robot Learning Methodology A reinforcement learning algorithm (Learning Automata) is used to search for a gait using the dynamic model built using MATLAB/SIMULINK/SimMechanics. The proposed solution is evaluated using the real robot. The performance of the simulated/real robots are compared. 3/10 3

Problem Formulation The movement of each joint is described by a function with linearly interpolated NE points and a period T. Complexity reduction: Similar legs use the same functions for each joint but with different time lags. Example: 4 legged robot: 4 similar legs (NP=4); 3 joints per leg (NA=3); 4 points in each function (NE=4). From 48 to 16 (4*3+4) variables. 4/10 4

Criterion for Similarity: Simmetry Distances of each leg to the robot CM: 5/10 5

Representation and Learning Function Description Start Selection of possible solution Test on the simulated robot Evaluation of the response Adjustment of the probabilitiy matrices Convergence? End Lag for leg Period Possible Periods 6/10 6

Functions learned for a tripod robot 7/10 7

Experimental Validation Quadruped robot, Tripod robot, Biped robot, Hybrid robot with 4 legs (2 joints per leg) and unactuated wheels in each foot. 8/10 8

Possible Lines for Future Work Conclusions GOOD: Several good solutions were found for each of the 4 cases tested so far (flat surfaces). BAD: The designer has to: set several parameters for the learning algorithm, e.g. min/delta/max values for each joint, lag and period, test different foot-ground friction models. Possible Lines for Future Work Test the proposed solution using larger robots with more powerful actuators and in more complex situations, e.g. going up and down inclined surfaces/staircases and running in rough terrain (grass using small/large feet). Use the comparison between the simulated and real robots to improve the simulation model and search for better solutions (outer optimization loop). 9/10 9

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