Real-time obstacle avoidance for manipulators and mobile robots
International Journal of Robotics Research
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Discrete mathematics and its applications (2nd ed.)
Discrete mathematics and its applications (2nd ed.)
Harmonic functions and collision probabilities
International Journal of Robotics Research
A Procedure for Detecting Intersections of Three-Dimensional Objects
Journal of the ACM (JACM)
Feature tracking in video and sonar subsea sequences with applications
Computer Vision and Image Understanding - Special issue on underwater computer vision and pattern recognition
Robot Motion Planning
Solid Modeling with Designbase: Theory and Implementation
Solid Modeling with Designbase: Theory and Implementation
Real-Time Systems
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
On the moving-obstacle path-planning algorithm of Shih, Lee, and Gruver
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A note on “Solving the find-path problem by good representation of free space”
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Real-time map building and navigation for autonomous robots inunknown environments
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Optimal task execution times for periodic tasks using nonlinear constrained optimization
The Journal of Supercomputing
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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.