Joint-space dynamics algorithm of space manipulators with tree structure by using inertia mapping matrix

This study, relevant to the development of appropriate trajectory planning and control algorithms, focuses on a modeling scheme that uses the concepts of graph theory and spatial notation for calculating the joint-space dynamics of tree structure space manipulator systems. Firstly, the configuration description of space manipulators using graph theory, the parent array, and path matrix is introduced. Secondly, based on the concept of generalized link, the spatial notation and composite rigid body are presented. Thirdly, the Composite Rigid Body Algorithm (CRBA) is exhibited. The Inertia Mapping Matrix (IMM) is then derived from the path matrix, which can be used to analyze the sparsity of the inertia matrix and the complexity of the CRBA algorithm. Within the context, a modified CRBA combines ideas of IMM and spatial notation is proposed to calculate the dynamics of tree structure space manipulators. Its computational procedure and complexity by using IMM are analyzed. Finally, a case study and comparison by using a humanoid configuration for branched and un-branched chains particularly verify the effectiveness and potential of the proposed modified CRBA for the space manipulators. Copyright