Modular and Hybrid Numerical-Analytical Approach - A Case Study on Improving Computational Efficiency for Series-Parallel Hybrid Robots

Modeling closed loop mechanisms is a necessity for the control and simulation of various systems and poses a great challenge to rigid body dynamics algorithms. Solving the forward and inverse dynamics for such systems require resolution of loop closure constraints which are often solved via numerical procedures. This brings an additional burden to these algorithms as they have to stabilize and control the loop closure errors. In order to avoid this issue, analytical solutions are preferred for commonly studied parallel mechanisms. This paper has two contributions. Firstly, it reports a case study on a modular and hybrid numerical-analytical approach to model and control series-parallel hybrid robots which are subjected to large number of holonomic constraints. The approach exploits the modularity in the robot design to combine analytical loop closure for the known submechanisms and numerical loop closure for submechanisms where analytical solutions are not available. This offers an edge over purely numerical approach in terms of computational efficiency. Secondly, an adaption of the constraint embedding approach in Articulated Body Algorithm (ABA) is presented which yields a recursive algorithm in minimal coordinates for computing the forward dynamics of series-parallel hybrid systems. The proposed modification exploits the Lie group formulations and allows easy implementation of recursive forward dynamics of constrained systems in state of the art multi-body solvers.