A collision modeling method for multiple manipulators task planning using shadow space

For the cooperative task planning of multiple manipulators, it is very important to check the collisions among the links and the end-effectors of the manipulators on their movement routes. This paper aims to propose a novel collision check method for multiple manipulators using the concept of a shadow space. The shadow space is defined as the space that a manipulator sweeps while moving in a 3-dimentional workspace. The workspace is discretized into MxNxL voxels; then, the discretized workspace is explicitly represented as a rank-3 tensor, which is named a shadow space tensor. When a manipulator moves from one task point to another, the shadow space tensor contains the spatial information with respect to the shadow space of the manipulator during the movement. Hie collision conditions among the manipulators can be simply detected using their shadow space tensors. This paper presents a defnution of a problem about the collision detection among multiple manipulators and proposes the collision checking method using the shadow space tensors. Then, the proposed method is validated through 3D robot simulation.