Control of motion and compliance

This chapter reviews different methods for the control of legged locomotion with a special focus on bipedal locomotion. All locomotion systems are governed by complex nonlinear, hybrid dynamics, and are redundant, underactuated and often unstable, which makes their control a very challenging task.The chapter starts with a presentation of different concepts of stability and robustness of locomotion considering nominal walking situations as well as the reaction to larger external perturbations. Then, optimal control is discussed as a guiding principle of human and robot motion, and dynamic multibody system models as well as different optimization problem formulations for the generation, control and analysis of locomotion are shown. Constant or variable compliance plays an important role in biological and bio-inspired locomotion, but needs to be properly adapted in the design and control process which also can be addressed by optimal control. Next, impedance control in locomotion is discussed, looking at passive and active impedance and different approaches to emulated appropriate impedances for robots. The chapter also reviews control approaches for legged locomotion based on template models, i.e. very simple representations of the original locomotor system, with a focus using template models for the design of suitable controllers. The state of the art of passive dynamic walking robots as well as powered and almost passive dynamic robots is summarized and their achievements in terms of energy-efficiency, stability, robustness and versatility re discussed. Hybrid zero dynamics is presented as a control synthesis framework that reduces the complexity of whole-body dynamics control and allows to develop efficient controllers for dynamic walking and running motions. Finally, a control approach for locomotion based on the concept of central pattern generators is presented which helps to control locomotion of legged robots and gives insight into human movement control.