Optimal Velocity Planning of Wheeled Mobile Robots on Specific Paths in Static and Dynamic Environments

The control system of a mobile robot generally comprises two different modules: a trajectory planner and a trajectory tracking controller, although some researchers have proposed algorithms that integrate both tasks. To completely solve the trajectory planning problem is to define an open-loop path and its velocity profile from an initial to a final posture, while avoiding any potential obstacles. In time-optimal planning of a wheeled mobile robot (WMR), the problem is solved by defining control inputs for the wheels that minimize navigation time from the origin to the target posture. This goal implies two tasks, which can be carried out simultaneously or sequentially: path-planning (PP), which involves the computation of the shortest feasible path; and velocity-planning (VP), which involves the computation of the fastest feasible velocity profile for the entire domain of the path. Several approaches have been developed to perform both tasks. The most widely used approaches are free configuration-time space based methods, (Reinstein & Pin, 1994), but these algorithms are computationally expensive, even when one is only dealing with PP or VP separately. To reduce the computational cost, researchers have recently published methods which do not require computing the C-space obstacles (Wang et al., 2004), as well as methods that search for a probabilistic road map (LaValle & Kuffner, 2001). Some other approaches that use intelligent computing-based methods have also been presented, such as those that use artificial potential fields-based methods (Liu & Wu, 2001), fuzzy logic (Takeshi, 1994), genetic algorithms (Nerchaou, 1998) or neural networks (Zalama et al., 1995). In order to find an optimal and feasible solution for the two problems, mechanical, kinematic and dynamic characteristics of the WMR that limit its motion must be taken into account, as well as other environmental, task-related and operational issues. These constraints can be summarized by upper boundary functions of the velocity, acceleration and deceleration of the WMR. In general, the functions are not constant, nor are they even continuous. They are therefore nonintegrable constraints, and the time optimal planning is a nonholonomic problem. A significant number of nonholonomic constraints, which include not only mechanical and kinematic but also dynamic characteristics of the WMR, are difficult to deal with when PP and VP are approached simultaneously. The vast majority of existing algorithms consider