image CHAPTER 4

Accounting for Body Dynamics: The Jogger's Problem

Let me first explain to you how the motions of different kinds of matter depend on a property called inertia.

— Sir William Thomson (Lord Kelvin), The Tides


As discussed before, motion planning algorithms usually adhere to one of the two paradigms that differ primarily by their assumptions about input information: motion planning with complete information (Piano Mover's problem) and motion planning with incomplete information (sensor-based motion planning, SIM paradigm, see Chapter 1). Strategies that come out of the two paradigms can be also classified into two groups: kinematic approaches, which consider only kinematic and geometric issues, and dynamic approaches, which take into account the system dynamics. This classification is independent from the classification into the two paradigms. In Chapter 3 we studied kinematic sensor-based motion planning algorithms. In this chapter we will study dynamic sensor-based motion planning algorithms.

What is so dynamic about dynamic approaches? In strategies that we considered in Chapter 3, it was implicitly assumed that whatever direction of motion is good for the robot's next step from the standpoint of its goal, the robot will be able to accomplish it. If this is true, in the terminology of control theory such a system is called a holonomic system [78 ...

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