An optimal control strategy for trajectory generation of industrial palletizers

This thesis is the result of a collaboration with SACMI Tech, a branch of SACMI Imola scrl. The objective of this work is the development of a trajectory generation strategy for industrial palletizers based on optimal control techniques. The main contribution is the design of an optimal control algorithm capable of generating a (practically) time-optimal trajectory, i.e., a trajectory for the palletizers that minimizes the travel time between the loading station and the offloading pallet. Notably, this trajectory must satisfy a number of constraints in order to be feasible for the real system and safe towards collisions. Here we consider an approximate version of classical minimum-time optimization problems (i.e., where time is an optimization variable) which are, in general, very hard to solve. Instead of looking for a minimum time trajectory, we approximate the original problem by setting up an optimal control problem to track a reference that travels at maximum speed the minimum distance path between the start and goal points. This simplified cost function allows us to use a simpler optimization algorithm that requires less computational effort to produce a result. The palletizer is working continuously by executing a series of tasks that requires a feasible trajectory for the machine to follow. This means that the algorithm must be able to address real-time constraints given by the palletizer and, when executed, must be able to generate a result within a deadline. Due to the high efficiency of the optimization algorithm, we are able to produce a result in a small amount of time (on average within a second), but if it's not able to compute an optimal trajectory on time we must be able to return a feasible result to allow the palletizer to keep working. For this reason, by using an efficient generation strategy for feasible trajectories we are always able to return a trajectory to the machine in order to perform the desired movement.