On Performance and Stability in Open- Loop Running a Dissertation Submitted to the Department of Mechanical Engineering and the Committee on Graduate Studies of Stanford University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

iii I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. I certify that I have read this dissertation and that in my opinion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Abstract Legged robots can provide access to hazardous environments such as waste sites, disaster areas and even the surfaces of other planets, where large obstacles and uneven terrain impede mobility with traditional wheeled systems. Looking to nature for design inspiration , a family of hexapedal robots has been developed that rely on passive mechanical properties and a simple open-loop motor control program to achieve fast and robust performance that begins to compare to that seen in nature. These robots are capable of running at over 4 body-lengths/second and can overcome hip-height obstacles without significantly slowing down. Although this approach works well for a range of open-loop parameters, the question of how to "tune" the system to achieve maximum performance while maintaining stability, especially as conditions change, arises. This thesis analyzes the trade-offs in stability and performance for open-loop running systems like the robots starting with simplified one and two degree-of-freedom dynamic models. Analyses of these models are then validated with experimental data of the running hexapods. Results reveal conditions for optimal performance and demonstrate inherent limitations in the use of open-loop control in running. Based on these findings, strategies for adaptation, or self-tuning, of the open-loop motor program are proposed that require only simple, low-band-width sensory feedback. One of these strategies is demonstrated experimentally in the adaptation of stride period in a hexapedal running robot. v For my real-life superheroes: my parents, Winston and Cecilia vi Acknowledgments