Logarithmic complexity dynamics formulation for computed torque control of articulated multibody systems

Divide-and-Conquer Algorithm is extended and integrated with the method of Computed Torque Control (CTC) to model and control fully-actuated multibody systems. CTC uses inverse and forward dynamics to control a multibody problem. This may impose unnecessary computational cost on the simulation if the corresponding equations are not formed and solved wisely. Additionally, this technique mainly uses the dynamic equations formulated based on the minimum number of joint coordinates. Herein, the Generalized Divide-and-Conquer Algorithm (GDCA) with the capability of accommodating both spatial and generalized forces is used to efficiently form the forward dynamic equations. Furthermore, a new mathematical formulation is generated to adjust the inverse-GDCA containing a redundant set of spatial and generalized coordinates with the joint-coordinate-based inverse dynamics utilized in CTC. Both GDCA and iGDCA apply a series of assembly and disassembly passes to form and solve the forward and inverse dynamic equations without generating the mass and Jacobian matrices of the entire system. This paper also addresses the challenges which may appear in controlling fully-actuated multibody systems with kinematic loops. The GDCA-based CTC is then equipped with popular control techniques such as PID, pole-placement-based state feedback, and linear quadratic regulator, and used to control selected multibody systems.