ABSTRACT

This chapter provides a survey of some of the techniques which have been used in planning paths for nonholonomic systems. It gives a bit more detail about some of the various methods of nonholonomic motion planning being pursued in the literature. The chapter considers paths for a car that cause a net rotation of any angle, or a translation in the direction that the car is facing. It explores the use of sinusoidal input signals for steering second- and higher-order model control systems. The chapter discusses the use of piecewise constant inputs to solve the general motion planning problem. It describes the rudiments of a method for motion planning for general nonholonomic systems due to Lafferriere and Sussmann. The chapter describes the use of some techniques from classical differential geometry which can be brought to bear on the specific problem of rolling a spherical finger on a planar surface.