ABSTRACT
This chapter provides a summary of classical path planning methods and an overview of state of the art methods for optimal trajectory planning, in particular such that they can be implemented in current industrial controller hardware. It discusses the main differences of the solutions proposed in the literature as well as a specific strategy. In addition to structurally compliant robotic systems, the chapter describes the motion planning for kinematically redundant serial robots. It is dedicated to collision avoidance and methods to incorporate the existence of obstacles within the workspace into the optimization problem. The term spline originates from the field of naval architecture, where thin flexible wooden or metal laths (called splines) were used to define the shape of a ship. The first known reference to smooth, piecewise-defined polynomials as splines was in 1946 by I. J. Schoenberg. The motion planning problem is frequently divided into the geometric path planning in task or configuration space and the trajectory planning.
