Optimal Trajectory Generation for Stewart Platform using Discrete Mechanics and Optimal Control

In this paper, we implement Discrete Mechanics and Optimal Control (DMOC) method to generate optimal trajectory for Stewart platform. Unlike conventional optimization method, this method directly exploits variational mechanics of systems using discrete form of Lagrange-d'Alembert principle. This discrete formulation serves as nonlinear constraints for relationship between discrete forces and discrete via points of trajectory. After detailed symbolic computation, we represent the complexity of Lagrangian-Based discrete mechanics of Stewart Platform in generalized coordinates. Finally, in order to avoid huge actuator forces in vicinity of kinematic singularity poses in workspace, we choose minimum actuator forces as optimization objective and optimal numerical results are compared with other known techniques.