A method for mapping the boundaries of collision-free reachable workspaces

作者：Yang Xiangdong^*; Wang Hongbo; Zhang Chuanqing; Chen Ken

来源：Mechanism and Machine Theory, 2010, 45(7): 1024-1033.

DOI：10.1016/j.mechmachtheory.2010.02.002

• Manipulator
• Workspace
• Collision-free reachable workspace
• Convex optimization
• Continuation method

This paper proposes a method for mapping the boundaries of manipulators' collision-free reachable workspaces. Knowledge of manipulators' actual available workspaces is important in applications and design, e. g., the pre-surgery planning for medical robots, the design parameter optimization for manipulators, etc. Algorithms for mapping the boundaries of reachable workspaces have been well developed in previous works, but we have not seen any method that takes into account the obstacles' effects on the manipulators' available workspaces. In this paper, the concept of collision-free reachable workspace is delivered. The obstacle and the end-effecter are modeled as intersections of convex implicit surfaces, which in this paper are defined as convex superquadrics. The minimum distance query between each two superquadrics is collapsed to a convex optimization problem. By employing an interior-point method, the collision-free conditions are obtained and integrated with the continuation method, creating an algorithm which enables the boundary mapping of collision-free reachable workspaces. To demonstrate and validate our approach, a planar three-bar manipulator is tested with the proposed algorithm; the boundaries of the manipulator's collision-free reachable workspaces are calculated and compared with the results of the manipulator's reachable workspaces.

• 出版日期2010-7
• 单位清华大学