Optimal Motion Generating of VV Nonholonomic Manipulators with Elastic Revolute Joints in Generalized Point-to-Point Task

This paper presents optimal control method to path planning of mobile robots with flexible joints. Dynamic equations are derived and additional kinematic constraints are used to solve the extra Dofs arose from base mobility. Then with modeling the elasticity at each joint as a linear torsinal spring, the set of equations are formed. The Hamiltonian function is formed and the necessary conditions for optimality are derived from the Pontryaginʹs minimum principle. The obtained equations established a two point boundary value problem solved by numerical techniques. This problem is known to be complex in particular when combined motion of the base and manipulator, non-holonomic constraint of base and non-linear and complicated dynamic equations as a result of flexible nature of joints are taken into account. The study emphasizes on modeling of the complete optimal control problem by remaining all nonlinear state and costate variables as well as control constraints to establish accompanying boundary value problem. Another advantage of this method is obtaining various optimal trajectories with different characteristics by changing the penalty matrices values which enables the designer to choose the best trajectory. A mobile flexible joint manipulator is studied to verify the feasibility of the proposed approach.