Nonlinear model predictive control of an overhead laboratory-scale gantry crane with obstacle avoidance

Gantry cranes are complex nonlinear electromechanical systems representing a challenging control problem. We propose an optimization-based controller for guiding the crane through arbitrary obstacles. Solving path planning problems with obstacles typically requires a two-stage approach. First, a path is found that is feasible w.r.t. system dynamics and obstacles. The path is then interpreted as a series of set points by a lower-level controller that guides the system. We instead generate a path, and the associated control input to move along that path, from a single optimization problem using a nonlinear model predictive control framework. In doing so, we generate a trajectory that is locally optimal and feasible w.r.t. system dynamics and obstacles. Multiple obstacle avoidance constraint formulations are proposed as smooth, differentiable functions. Objects are approximated either as the union of a set of smooth shapes or as smooth indicator functions. The formulations presented in this work are applicable to (non) convex problems in 2-D or 3-D spaces. Numerical methods are used to solve the proposed problems for both 2-D (fixed string length) and 3-D (varying string length) models of the gantry crane, resulting in consistently lower costs than nodal or sampling based algorithms.