Real-Time Trajectory Generation for a Planar Crane using Discrete Mechanics

We present a receding horizon control scheme that utilizes a discrete time version of a nonlinear, iterative, projection-based optimization routine. The routine utilizes a projection operator to ensure feasible system trajectories at each iteration of the optimization resulting in valid control signals even when constraints on computation time prevent full convergence. An additional feature of this work is that the underlying discrete time system representation is provided by a discrete mechanics derived variational integrator as opposed to, e.g., a Runge-Kutta based integrator. Recent work has described a midpoint variational integrator that provides a causal, onestep map that admits both first and second order linearizations facilitating use in standard discrete time control and estimation techniques such as linear quadratic regulators and extended Kalman filters. In this work, this variational integrator is combined with the aforementioned receding horizon optimization routine to generate feasible system trajectories for real-time control of an experimental planar crane system.