Metoder för rörelseplanering och analys av underaktuerade mekaniska system och redundanta manipulatorer

Motion planning and control synthesis are challenging problems for underactuated mechanical systems due to the presence of passive (non-actuated) degrees of freedom. For those systems that are additionally not feedback linearizable and with unstable internal dynamics there are no generic methods for planning trajectories and their feedback stabilization. For fully actuated mechanical systems, on the other hand, there are standard tools that provide a tractable solution. Still, the problem of generating efficient and optimal trajectories is nontrivial due to actuator limitations and motion-dependent velocity and acceleration constraints that are typically present. It is especially challenging for manipulators with kinematic redundancy. A generic approach for solving the above-mentioned problems is described in this work. We explicitly use the geometry of the state space of the mechanical system so that a synchronization of the generalized coordinates can be found in terms of geometric relations along the target motion with respect to a path coordinate. Hence, the time evolution of the state variables that corresponds to the target motion is determined by the system dynamics constrained to these geometrical relations, known as virtual holonomic constraints. Following such a reduction for underactuated mechanical systems, we arrive at integrable second-order dynamics associated with the passive degrees of freedom. Solutions of this reduced dynamics, together with the geometric relations, can be interpreted as a motion generator for the full system. For fully actuated mechanical systems the virtually constrained dynamics provides a tractable way of shaping admissible trajectories. Once a feasible target motion is found and the corresponding virtual holonomic constraints are known, we can describe dynamics transversal to the orbit in the state space and analytically compute a transverse linearization. This results in a linear time-varying control system that allows us to use linear control theory for achieving orbital stabilization of the nonlinear mechanical system as well as to conduct system analysis in the vicinity of the motion. The approach is applicable to continuous-time and impulsive mechanical systems irrespective of the degree of underactuation. The main contributions of this thesis are analysis of human movement regarding a nominal behavior for repetitive tasks, gait synthesis and stabilization for dynamic walking robots, and description of a numerical procedure for generating and stabilizing efficient trajectories for kinematically redundant manipulators