Using Soft Computing Techniques for Improving Foot Trajectories in Walking Machines ••••••••••••••••••• •••••••••••••••• Elena Garcia*, Pablo Gonzalez-de-Santos Instituto de Automatica Industrial-CSIC La Poveda, 28500 Arganda del Rey Madrid, Spain Received 30 May 2000; accepted 27 February 2001 Walking machines have been investigated during the last 40 years and some basic techniques of this field are already well known. However, some aspects still need to be optimized. For instance, speed seems to be one of the major shortcomings of legged robots; thus, improving leg speed has been chosen as the main aim of this work. Although some algorithms for optimizing trajectory control of robot manipula- tors already exist, we propose a more computationally efficient method that employs fuzzy set theory to involve real dynamic effects over leg motion instead of an inaccu- rate mathematical model. In this article, we improve leg speed by automatically tuning the acceleration of legs. For this purpose, we define fuzzy rules based on experiments and we find the optimal acceleration for every given trajectory. A simple fuzzy infer- ence system is used to compute the required acceleration. It is based on five rules using three linguistic variables. Final results show that foot acceleration tuning for straight trajectory generation is a suitable method for achieving accurate, smooth and fast foot movements. Also it is shown that under some conditions average leg speed can be increased up to 100% using the control methods herein proposed. © 2001 John Wiley & Sons, Inc. 1. INTRODUCTION Legged robots have been extensively investigated during the last four decades, and activity in this field is still increasing. Work in these years was mainly *To whom all correspondence should be addressed; e-mail: egarcia@iai.csic.es. Contract Grant Sponsor: CICYT (Spain). Contract Grant number: TAP1999-1080-C04-01. concentrated on the design of leg mechanisms and machine structures, and some areas of knowledge are quite well known now, such as the genera- tion of continuous, 1 discontinuous 2 and free 3 stati- cally stable gaits. There is also great activity in the understanding of living walking locomotion. Zoolo- gists and biologists are becoming interested in this technology and they are trying to apply biological understanding to the design and control of walking machines. 45 Journal of Robotic Systems 18(7), 343–356 (2001) © 2001 by John Wiley & Sons, Inc.