A realistic method for real-time obstacle avoidance without the Calculation of Cspace Obstacles

An important concept proposed in the early stage of the robot path planning field is the shrinking of a robot to a point and meanwhile the expanding of the obstacles in the workspace as a set of new obstacles. The resulting grown obstacles are called the Configuration Space (Cspace) obstacles [24, 23]. The find-path problem is then transformed into that of finding a collision-free path for a point robot among the Cspace obstacles. However, the research experiences obtained so far have shown that the calculation of Cspace obstacles is very hard when the following situations occur: 1. both the robot and obstacles are not polygons and 2. the robot is allowed to rotate. This situation is getting even worse when the robot and obstacles are three dimensional (3D) objects with various shapes [43, 54, 3]. Obviously, a direct path planning approach without the calculation of the Cspace obstacles is strongly needed. This paper presents such a new real-time robot path planning approach which, to our best knowledge, is the first one in the robotic community. Motivated by the practical requirements of obstacle representation, a generalized constrained optimization problem (GCOP) with not only intersection but also union operations was proposed and a mathematical solution to it was developed [47]. This paper inherits the fundamental ideas of inequality and optimization techniques from the previous work [45-47] and converts the real-time obstacle avoidance problem into a semi-infinite constrained optimization problem with the help of the mathematical transformation given in [47]. This leads to an efficient method for the real-time obstacle avoidance. Simulation results in 3D space have been presented to show its merits.