Control of spring-mass running through virtual tuning of leg damping

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2020
Seçer, Görkem
Spring-mass models have been very successful in both describing and generating running behaviors. In this regard, the Spring-Loaded Inverted Pendulum (SLIP) is a useful model to represent hybrid dynamics of both natural and robotic runners. Existing research on dynamically capable legged robots, particularly those based on this model, generally considers improving in isolation the stability and control accuracy on the rough terrain or the energetic efficiency in steady state. On the other hand, the pure SLIP model is energetically conservative, hence being unable to define a way for modulation of running energy in legged robots. In this thesis, we propose a new method based on incorporating a virtually tunable leg damping onto the SLIP template model in order to control running energy while addressing both accuracy and efficiency. In the first part of this thesis, we present our theoretical approach. Proposing to extend the basic SLIP model with a once per step tunable leg damping, we show that energy can be effectively controlled for a vertical hopping task. After showing invertibility of step-to-step Poincare map, we formulate a deadbeat controller with single step convergence. Then, we generalize this controller to planar running, which requires decomposition of the control problem into two coupled subproblems: the regulation of system energy, and the distribution of this energy among different degrees of freedom in the system. The rest of this part focuses on how to efficiently solve this problem, minimizing the energetic expenditure as well as the required computational power. To this end, we preserve the validity of the existing analytic approximations to the underlying SLIP model, propose improvements to increase the predictive accuracy, and construct accurate, model-based controllers that use the tunable damping coefficient of the template model. This part concludes with results of extensive comparative simulations to establish the energy and power efficiency advantages of our approach, together with the accuracy of model-based gait control methods. In the second part of this thesis, we experimentally verify our theoretical claims. To this end, we, first, build a vertical hopping robot with series elastic actuation. After formulating a set of feasibility constraints towards implementation on such robotic platforms, we optimize our approach with a new gait controller allowing to use the entire stance phase for injection/removal of energy, decreasing the maximum necessary actuator power for series-elastically actuated robotic platforms while eliminating wasteful sources of the negative work altogether. Enabling the most efficient use of actuator power in this manner while preserving analytic tractability, we then show through high fidelity simulations of the robotic platform that the proposed strategy establish substantial performance gains with respect to all available alternatives. Furthermore, experimental evaluation of this approach shows that numerical results translate to the hardware, hence verifying our theoretical claims. Finally, we present our efforts towards implementation of the proposed gait controller on ATRIAS biped, which is a compliant humanoid robot with point feet. Preliminary experimental investigation on this platform reveals that our approach can provide accurate control of running on a complex bipedal robot.
Citation Formats
G. Seçer, “Control of spring-mass running through virtual tuning of leg damping,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Chemical Engineering., Middle East Technical University, 2020.