On-Line Collision-Avoidance Trajectory Planning of Two Planar Robots Based on Geometric Modeling

Superquadric modeling technology applied to the description of various shapes of robot links is discussed in the paper. Through a series of homogeneous transformations between the robots’ links, which have been modeled as a specified superquadric form, ellipse, the complexity of the collision detection problem can be reduced when evaluating the relative location between a transformed ellipse and a point. To cope with the analytic method, a spatial measurement between two objects called the collision probability, instead of the Cartesian distance, is defined by projecting the geometric similarity of an elliptic equation onto the contour of the Gaussian distribution. This probability represents the sensitivity of collision occurrance. The proposed algorithm is implemented in an environment where the on-going paths of the robots are fixed, but their speeds are alternative. Therefore, an objective function is defined to refine the optimal points along the paths for each sampling time, which, hence, forms the collision-free trajectories for the cooperative robots.