Optimization-Based Control Approaches to Humanoid Balancing

Abstract

Balance is an essential feature of humanoids but, despite a strong understanding of its laws and dynamics, it remains an open problem for control applications. Optimization-based control approaches explicitly include balance dynamics and constraints in the control problem in order to capture at best the behavior of the system and fully exploit it to reach complex control objectives. Although theoretically appealing, these approaches intrinsically induce a significant computational burden. In practice, this implies to resort to simplifications on the model and problem complexities, which limits the capacity to actually generate complex behaviors. In this chapter, an overview of the balance problem is first proposed. A general, abstract formulation of the balance control problem as an optimal control one is then derived. Three major approaches can be found in the literature, coping with the computational complexity of the general balance optimization problem. They range from offline motion planning to reactive whole-body control and are presented in the remainder of the chapter.