Robotics Research Technical Report: Analysis of the Motion-Planning Problem for a Simple Two-Link Planar Arm (Classic Reprint)

Excerpt from Robotics Research Technical Report: Analysis of the Motion-Planning Problem for a Simple Two-Link Planar Arm

Define the forearm PQ to be an oriented segment of length dz, with elbow P. A place ment of the arm is a pair where X is the position of P and 0 is the orientation of pq. The free room V is the open polygonally bounded region given by room interior less the obstacles. A real wall is a boundary segment of V. The workspace F is the largest Open star shaped region with center at O contained in V. F is clearly polygonally bounded and is cut out of V by segments each originating at an obstacle corner and directed away from 0. We refer to these segments as virtual walls; from now on 'wall' will mean a real or-'virtual wall.

Clearly, P must stay within F since the line-segment OP (the upper arm) must stay within V.

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