A Generalized Real-Time Obstacle Avoidance Method Without the Cspace Calculation

An important concept proposed in the early stage of robot path planning field is the shrinking of a robot to a point and meanwhile the expanding of obstacles in the workspace as a set of new obstacles. The resulting grown obstacles are called the Configuration Space (Cspace) obstacles. 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 have shown that the Cspace transformation 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 gets even worse when the robot and obstacles are three dimensional (3D) objects with various shapes. For this reason, direct path planning approaches without the Cspace transformation is quite useful and expected. Motivated by the practical requirements of robot path planning, a generalized constrained optimization problem (GCOP) with not only logic AND but also logic OR relationships was proposed and a mathematical solution developed previously. This paper inherits the fundamental ideas of inequality and optimization techniques from the previous work, converts the obstacle avoidance problem into a semi-infinite constrained optimization problem with the help of the mathematical transformation, and proposes a direct path planning approach without Cspace calculation, which is quite different from traditional methods. To show its merits, simulation results in 3D space have been presented.