In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering

This thesis demonstrates the successful application of Virtual Model Control (VMC) to a simulated sevenlink planar biped for walking dynamically and steadily over sloped terrain with unknown slope gradients and transition locations. The slope gradients were assumed to be between ± 200; and it had maximum transitional gradient change of less than 200 per step. The developed algorithm for sloped terrain walking was based on a level ground implementation with only minor changes. This thesis adopted the same virtual components, which included a vertical spring-damper, a horizontal damper and a rotational spring-damper, to generate the required torque at the joints. The biped used the natural compliance of swing foot so that it could land flat onto an unknown slope. After the complete touch down of the swing foot, a global slope was computed and this was used to define a virtual surface. The algorithm then computed the desired hip height based on the global slope which resulted in a desired straight line trajectory parallel to the virtual surface. The algorithm was very simple and did not require the biped to have an extensive sensory system for blind walking over slopes. The ground was detected only through foot contact switches. The knowledge required for the implementation mainly consisted of intuition and geometric considerations. This thesis also demonsrates the replacement of the vertical virtual spring-damper with Robust Adaptive Controller and the successful implementation with the biped walking over random sloped terrain. This thesis also shows how the algorithm for sloped terrain walking can be extended to stair climbing. Thesis Supervisor: Gill A. Pratt, Ph.D. Title: Assistant Professor of Electrical Engineering and Computer Science