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This paper presents a method for building a foothold selection module as well as methods for the stability check for a multi-legged walking robot. The foothold selection decision maker is shaped automatically, without expert knowledge. The robot learns how to select appropriate footholds by walking on rough terrain or by testing ground primitives. The gathered knowledge is then used to find a relation between slippages and the obtained local shape of the terrain, which is further employed to assess potential footholds. A new approach to function approximation is proposed. It uses the leastsquares fitting method, the Kolmogorov theorem and population-based optimization algorithms ; A strategy for re-learning is proposed. The role of the decision support unit in the control system of the robot is presented. The importance of the stability check procedure is shown. A method of finding the stability region is described. Further improvements in the stability check procedure due to taking into account kinematic correction are reported. A description of the system for calculating static stability on-line is given. Methods for measuring stance forces are described. The measurement of stance forces facilitates the extended stability check procedure. The correctness of the method is proved by results obtained in a real environment on a real robot.