Efficiënte bewegingsplanning voor robottoepassingen: een aanpak op basis van optimale controle

Due to their autonomous capabilities and their large potential to replace and support humans in all aspects of life, robots, the situations where they are deployed and the tasks that they have to perform are becoming increasingly complex. This pushes control algorithms to evolve similarly in complexity,<br />enabling robots to autonomously handle a large variety of tasks while meeting expectations of high performance and reliability. The performance of robotic applications is not only determined by several performance metrics but also by the robots adhering to their inherent limitations and the requirements imposed by the task. Optimal control problems (OCPs) and their reactive component - model predictive control (MPC) - handle these requirements naturally through their formulation of the control problem as an optimisation problem, allowing to balance desired performance objectives with hard constraints that must be satisfied. It enables control engineers to extract high performance out of a robotic system while guaranteeing adherence to the constraints and task requirements. However, despite their attractive properties, the adoption of optimal control and MPC for these complex applications is limited for various reasons. Firstly, the inherent computational complexity of solving an optimisation problem hinders the use of these techniques for complex systems as the low-level controllers of these systems often require control updates between 50 Hz and 1 kHz which are hard to meet for MPC. Secondly, due to its optimisation-based nature, optimal control is restricted in the representation and the size of the environments where the robot has to perform its task. These restrictions exist due to the disadvantageous scalability of the computational performance towards cluttered environments and the dependency on differentiable constraint and objective formulations. Lastly, implementing performant optimal control strategies requires a large engineering effort and a deep knowledge of optimisation. This thesis addresses those limitations by (1) reducing the computational complexity of optimal control for cluttered environments, (2) by facilitating the use of optimal control in an industrial context and (3) by lowering the computational requirements of MPC algorithms for complex systems. First of all, it introduces a technique that reduces the amount of constraints in an OCP through only considering the most critical one at a time. It also reformulates a generic obstacle avoidance constraint to simplify the formulation of collision avoidance for a set of obstacle geometries. Through extensive experimentation, both techniques are shown to significantly reduce the computational complexity of solving an OCP with a negligible loss in optimality. The complexity reduction does not come at the expense of constraint satisfaction. Secondly, this thesis covers a methodology to relax the hard requirement on high control rates for MPC by asynchronously computing MPC updates at a slower rate and tracking those control updates with a low-level feedback controller at a high rate. The efficacy of this methodology, extended with a safety controller in case of MPC failure, is validated for autonomous agile quadrotor navigation in partially known, obstacle-rich environments. Lastly, this dissertation presents a computationally efficient motion planner for object picking in industry. The focus of the planner is on low computation complexity and easy-to-tune constraints that guarantee reaching a desired pick pose accuracy and that computes trajectories that are on average 30% faster than the state-of-the-art.