Geometric Methods in the Control of Bipedal Walking Robots

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The object of this project is to develop control algorithms for bipedal walking robots using concepts of geometric reduction. Geometric reduction takes advantage of certain symmetry properties in the dynamic equations of bipedal robots and facilitates the computation of lower dimensional models for analysis and control design. The goal is to enable control concepts developed for two-dimensional, or planar, bipeds to be applied to fully three-dimensional bipeds. In this way, the complexity of the control problem for three-dimensional walking robots is greatly reduced. The project will also investigate the effects of asymmetries in leg parameters, such as leg length and leg mass, on the existence and properties of passive gaits. Preliminary investigations indicate that asymmetry in leg parameters, such as leg mass, results in qualitative changes in gait, such as period-doubling bifurcations and chaotic motion. Deliverables from this research include new control algorithms, new simulation models and graphical simulation tools for visualization of simulation data.The practical application of this research is in the design of walking robots that have improved performance capabilities over existing machines. Current walking robots have limited range due to poor energy utilization and are limited in their ability to navigate uneven terrain. More practical and more efficient walking machines will result once the full power of available theoretical tools is brought to bear on the analysis and design questions in this project. The tools developed in this project will also contribute to a better understanding of human locomotion, which will result in applications in biomechanics and biomedicine, such as the design of improved prosthetic devices, the development of falls prevention programs for the elderly, and rehabilitation techniques. The study of bipeds with parameter asymmetry is motivated by the desire to understand the effect of asymmetry of human gait on walking stability, performance, and gait disorders. Our research results will also be used to create demonstrations and presentations for middle school and high school students to be used as recruiting tools. Our past experience has shown that robotics is an excellent vehicle to attract and retain students in engineering.