A model-based trajectory planning approach for flexible-link mechanisms

In this paper the problem of trajectory planning for flexible-links mechanisms is dealt with. The method proposed here is suitable for the determination of model-based optimal point-to-point trajectories with bounds on kinematic and dynamic characteristics of the mechanism. An open-loop optimal control strategy is applied to an accurate dynamic model of flexible multi-body planar mechanisms. The model, which has already benn fully validated through experimental tests, is based on finite element discretization and accounts for the main geometric and inertial nonlinearities of the linkage. Exploiting an indirect or variational solution method, the necessary optimality conditions deriving from the Pontryagin´s minimum principle are imposed, and lead to a differential Two-Point Boundary Value Problem (TPBVP); numerical solution of the latter is accomplished by means of collocation techniques. Considering a lightweight RR robot, simulation results are provided for rest-to-rest trajectories with bounded speed and bounded elastic deformation. However, the strategy under investigation has general validity and can be applied to other types of machanisms, as well as with different objective functions and boundary conditions.