Workspace Generation of Hyper-Redundant Manipulators as a Diffusion Process on<tex>$SE(N)$</tex>

Hyper-redundant manipulators have a large number of redundant degrees of freedom. They have been recognized as a means to improve manipulator performance in complex and unstructured environments. However, the high degree of redundancy also causes difficulty in the calculation of workspaces and inverse kinematics. This paper develops a diffusion-based algorithm for workspace generation of hyper-redundant manipulators. This algorithm makes the workspace generation problem as simple as solving a diffusion equation which has an explicit solution. This diffusion equation is a partial differential equation defined on the motion group SE(N), and describes the evolution of the workspace density function, depending on manipulator length and kinematic properties. This paper also solves the inverse kinematics problem in an elegant way by dividing the manipulator into virtual segments and cascading the corresponding workspace densities generated by the diffusion equation.