Multi-Dimensional Nonlinear Oscillation Control of Compliantly Actuated Robots

To increase performance and energetic efficiency, robot design recently evolved from classical, rigid to intrinsically compliant actuation. The introduction of elastic elements enables the absorption of external impact forces, and it offers the capability of buffering and directedly releasing kinetic energy. Therefore, the instantaneously retrievable power at the link side of the joint is not limited by the restricted input power of the motor. These properties can be exploited in the execution of highly dynamical, cyclic, and periodic motion tasks such as hammering, pick-and-place with robotic manipulators, walking, jumping, or running with versatile, articulated legs. Although compliant actuators are promising regarding performance and efficiency, they turn the plant into a multi-dimensional, nonlinear, oscillatory system, of which the analysis and control is a challenging task. This thesis contributes to the theory of energy-efficient limit cycle generation, dimensionality reduction of nonlinear systems, natural dynamics-based, modal controllers, and the application to legged system design and control. A new, robust control principle is proposed, which solves the problem of resonance-like excitation in the single-degree-of-freedom, nonlinear oscillator case. Thereby, existence, uniqueness, and attractiveness of resulting periodic orbits are proven based on novel statements, which contribute to hybrid dynamical system and contraction theory. To generalize these findings to multiple dimensions, classical results of theoretical mechanics suggest to reduce the dimensionality of the oscillatory dynamics to one. This proposition is further supported by empirical evidence of biologists that fundamental principles of legged locomotion are based upon oscillatory movements, which evolve on lower-dimensional submanifolds than the configuration space of articulated legs. The well-established method of modal analysis solves the problem of dimensionality reduction for the linear case. However, the multibody dynamics of articulated robots is strongly nonlinear, and therefore, linear modal analysis is not applicable straightforwardly. A novel theory of oscillation modes of nonlinear dynamics is proposed here, which solves the problem at hand for the general case. The main theorem on oscillation modes provides algebraically verifiable conditions, for which a one-dimensional submanifold of some configuration space represents an invariant set of the considered dynamical system. By means of this finding a method is introduced which allows to embody low-order, desired task dynamics as oscillation modes in the mechanical design of the robotic system. To exploit the natural oscillatory behavior, as given by oscillation modes, appropriate control methods are crucial. For this purpose, four different modal control methods are introduced, which address the demands of feasibility, versatility, robustness, and efficiency with varying priority. The control methods are validated in simulations and experiments. A proof of concept is performed by applying the theoretical results to the design and control of legged robots. Thereby, the performance and efficiency of the approach is experimentally validated in various dynamic locomotion gaits with compliantly actuated quadrupedal and bipedal robots. This is a fine step towards the vision to create a versatile and efficient system, which can efficiently move in rather simple terrain but has simultaneously the capability to climb, jump, and crawl in rough and challenging terrain, being therefore able to reach areas, where no other system could go before