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

This study 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. The objective is to investigate the forward and inverse multibody dynamics algorithms which are relevant to the development of appropriate trajectory planning and control algorithms. Rather than using conventional parent array as primary tool to analyze the sparsity and computational complexity of inertia matrix, this study combines ideas of graph theory and spatial notation, and presents a new analytical tool, namely inertia mapping matrix (IMM) for sparsity and complexity analysis. Firstly, the parent array and path matrix of space manipulator are introduced. Secondly, based on the concept of generalized link, the equivalence between standard 3 dimensional (3D) notation and spatial notation is proved. Thirdly, the IMM is derived from the path matrix and a modified composite rigid body algorithm (CRBA) is proposed to calculate the dynamics of space manipulator. Finally, branch-induced sparsity and computational complexity of inertia matrix are analyzed using path matrix and IMM. A case study and comparison for branched and un-branched chains is performed to verify the efficiency of the proposed algorithm.