Efficient formulation of inverse dynamics and control application to a planar variable geometry truss

Abstract

This paper addresses an efficient formulation of inverse dynamics and an application to the control of a planar variable geometry truss (VGT). The VGT is composed of many members in comparison to its degree of freedom (N), i.e., the number of generalized coordinates after constraints are considered, since the VGT has many topological closed loops. By using a Lagrangian method, an efficient order N formulation of the inverse dynamics is realized in this paper because the derived equations of motion have a recursive form. Furthermore, the derived equations contain geometric constraints due to the topological closed loops and we do not have to add calculations for those constraints. The proposed method needs fewer calculations in comparison with the Newton-Euler method with constraint equations. The effectiveness of the proposed method for inverse dynamics is examined by a numerical simulation as well as a hardware experiment of a resolved acceleration control. The experimental result successively shows that the controller using the proposed method is well implemented in the hardware system with one millisecond sampling time, and it achieves a good control performance comparable to that shown by a numerical simulation.