Nonholonomic Motion Planning

This last chapter addresses one of the most basic control issue: how to construct a control law steering a control system from a given state to another one? This problem is known as the motion planning problem. In the case of nonholonomic systems it can be solved exactly for specific classes of systems, in particular for nilpotent systems (Sect. 3.2). However for a general nonholonomic systems it is hopeless to look for exact solutions to the problem. Thus a solution must be thought as an algorithm which steers the system to an arbitrarily small neighbourhood of the goal. In this context a key notion is the one of approximation and we will see in Sect. 3.3 how the concepts introduced in the previous chapter allow to construct such an algorithm. We will also discuss two other methods in Sect. 3.4 and give an overview of the literature in Sect. 3.5.

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