Optimizing cell decomposition path planning for mobile robots using different metrics

Many robot planning approaches use cell decomposition methods for finding a sequence of regions that the robot should traverse. When a fully-actuated robot is used, the robot reference trajectory is simply constructed by linking through line segments the middle points of common facets of successive traversed cells. This paper improves this approach by proposing three different optimizations that yield the waypoints through which the robot piecewise linear route is passing. The optimizations use different metrics defined as sums of norms for the linear segments that compose the route. The norms L₁, L₂ squared and L_∞ are used and standard optimization problems result in each case. Examples are included for showing the usefulness of these optimizations, since shorter routes can be obtained under a negligible computational overhead.