Simulating underactuated multibody dynamics using servo constraints and variational integrators

Abstract

In underactuated dynamical systems, the number of control inputs nu is smaller than the number of degrees of freedom nq.Real world examples include e. g. flexible robot arms or cranes. In these two exmples the goal is to prescribe the trajectory of an end effector and find the necessary control variables. One approach to model these problems is to introduce servo constraints in the equations of motion that enforce a given trajectory for some part of the system [1].

Trajectory-tracking control from a multibody system dynamics perspective

“…The inverse model of differentially flat systems is given completely algebraically [39], while the inverse model of minimum phase systems has stable dynamics behavior and the inverse model of non-minimum phase systems has unstable system behavior [40,41]. Most literature on servo-constraints focuses on differentially flat systems, such as cranes [36,42,43], three-dimensional rotary cranes [37,44], and mass-spring chains [33,38,45,46]. Some literature also considers minimum phase systems, such as robotic manipulators with a few links [47,48].…”