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.

Smart structures research in Japan

“…Extending their previous works based on impedance control, they proposed an efficient formulation of inverse dynamics for an end effector of a structure with a large number of DOFs. In their formulation the complicated geometrical constraint conditions were included in the equation of motion which was given in a recursive form [15]. in [16], the virtual mass matrix of the end effector was used to evaluate an induced shock force at the moment of docking and to formulate an optimization problem in which the virtual mass was minimized.…”

“…in [16], the virtual mass matrix of the end effector was used to evaluate an induced shock force at the moment of docking and to formulate an optimization problem in which the virtual mass was minimized. Senda et al [17] also studied the impedance control of a redundant VGT structure in which the Jacobian matrix of the system was singular so that the controlled system may become unstable. To avoid instability and realize a desired impedance, the effect of the velocities of the actuators was fed back to the control force.…”