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Journal of Inforamtion Science and Engineering, Vol.15 No.1, pp.131-152 (January 1999)
On-Line Collision-Avoidance Trajectory Planning of Two
Planar Robots Based on Geometric Modeling

Kao-Shing Hwang and Ming-Dar Tsai
Electrical Engineering Department
National Chung Cheng University
Chiayi, Taiwan 621, R.O.C.

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.

Keywords: robotics, collision avoidance, geometric modeling, coordinate transformation, trajectory planning, collision probability

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Received August 15, 1996, accepted September 25, 1997.
Communicated by Zen Chen.