| A new approach for planning a feasible collision-free path based on a Bezier curve of order two, a parabola, has been developed for two- and three-dimensional environments. It is assumed that obstacles are stationary and the shape and location of obstacles are known. The algorithm involves geometric analysis and produces a path connecting a user specified start and target point which does not interfere with any obstacles. The algorithm consists of three parts: a geometric mapping of obstacles, selection of intermediate points, and smoothing of the final path.; A geometric mapping transforms obstacles in Euclidean space into obstacle images in the parameter space ({dollar}theta{dollar}, t). The main property of the geometric mapping is that a point in the parameter space which is not mapped by obstacle images, corresponds to a collision-free parabola in Euclidean space. If the entire parameter space is occupied by obstacle images, intermediate connection points are searched. Selections of intermediate connection points are made near the vertices of the obstacle that blocks the straight line connecting the start and target point. Geometric mapping is then carried out for each subinterval, and smoothing the slope discontinuity at each connection point is performed to ensure the overall smoothness of the curve.; Three supporting algorithms--expansion of obstacles, collision recognition, and change of configuration without changing the end-effector position--are developed for collision avoidance of a planar 3R robot and a General Electric P60 robot. Expansion of obstacles is introduced to accommodate the size of the end-effector. Collision recognition of robot links is carried out by checking interferences among robot links and obstacles. Change of configuration by rotating orientation of the end-effector, without altering the position, is introduced to alleviate the problems associated with an attempt to move out of the reachable workspace, exceed the valid range of joint-actuators or collide with obstacles.; Animated simulation of collision-free path generation and collision avoidance of a planar 3R robot and a General Electric P60 robot is implemented on a Silicon Graphics 4D/70 graphics workstation. |
