The first book dedicated to robot motion was published in 1982 with the subtitle "Planning and Control."5 The distinction between motion planning and motion control has mainly historical roots. Sometimes motion planning refers to geometric path planning, sometimes it refers to open loop control; sometimes motion control refers to open loop control, sometimes it refers to close loop control and stabilization; sometimes planning is considered as an offline process whereas control is real time. From a historical perspective, robot motion planning arose from the ambition to provide robots with motion autonomy: the domain was born in the computer science and artificial intelligence communities.22 Motion planning is about deciding on the existence of a motion to reach a given goal and computing one if this one exists. Robot motion control arose from manufacturing and the control of manipulators30 with rapid effective applications in the automotive industry. Motion control aims at transforming a task defined in the robot workspace into a set of control functions defined in the robot motor space: a typical instance of the problem is to find a way for the end-effector of a welding robot to follow a predefined welding line.
What kind of optimality is about in robot motion? Many facets of the question are treated independently in different communities ranging from control and computer science, to numerical analysis and differential geometry, with a large and diverse corpus of methods including, for example, the maximum principle, the applications of Hamilton-Jacobi-Bellman equation, quadratic programming, neural networks, simulated annealing, genetic algorithms, or Bayesian inference. The ultimate goal of these methods is to compute a so-called optimal solution whatever the problem is. The objective of this article is not to overview this entire corpus that follows its own routes independently from robotics, but rather to emphasize the distinction between "optimal motion" and "optimized motion." Most of the time, robot algorithms aiming at computing an optimal motion provide in fact an optimized motion that is not optimal at all, but is the output of a given optimization method. Computing an optimal motion is mostly a challenging issue as it can be illustrated by more than 20 years of research on wheeled mobile robots (as we discuss later).
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