Downloaded from

In this paper we generalize previous work in which the fixed points of dynamical systems were used to construct obstacle-avoiding, goalattracting trajectories for robots to more complex attractors such as limit cycles in the form of closed planar curves. Following the development of a formalism for dealing with a mechanical system, some of whose coordinates are constrained to follow the trajectories of a set of coupled differential equations, we discuss how to construct, analyze, and solve a planar dynamical system whose limit set is one or more user-specified closed curves or limit cycles. This work finds its relevance in a wide range of applications. Our focus has mainly been on planning tool trajectories for industrial robot manipulators with applications such as welding and painting. However, the generalization from fixed points to limit cycles is also applicable when controlling automatic guided vehicles. KEY WORDS—trajectory planning constraint mechanics, dynamical systems, limit cycles 1