Accelerated Spline-Based Time-Optimal Motion Planning with Continuous Safety Guarantees for Non-Differentially Flat Systems

Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion planning as a single Optimal Control Problem (OCP) but often suffer from high computational cost because they include separating hyperplane parameters as decision variables to enforce continuous collision avoidance. This paper presents a novel method that alleviates this bottleneck by decoupling the determination of separating hyperplanes from the OCP. By treating the separation theorem as an independent classification problem solvable via a linear system or quadratic program, the proposed method eliminates hyperplane parameters from the optimisation variables, effectively transforming non-convex constraints into linear ones. Experimental validation demonstrates that this decoupled approach reduces trajectory computation times up to almost 60% compared to fully coupled methods in obstacle-rich environments, while maintaining rigorous continuous safety guarantees.

Decoupling Collision Avoidance in and for Optimal Control using Least-Squares Support Vector Machines

This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal control problem (OCP) using the separating hyperplane theorem. By framing this theorem as a classification problem, the hyperplanes are eliminated as optimisation variables from the OCP. This effectively transforms non-convex constraints into linear constraints. A bi-level algorithm computes the hyperplanes between the iterations of an optimisation solver and subsequently embeds them as parameters into the OCP. Experiments demonstrate the approach's favourable scalability towards cluttered environments and its applicability to various motion planning approaches. It decreases trajectory computation times between 50\% and 90\% compared to a state-of-the-art approach that directly includes the hyperplanes as variables in the optimal control problem.

ASAP-MPC: An Asynchronous Update Scheme for Online Motion Planning with Nonlinear Model Predictive Control

This paper presents a Nonlinear Model Predictive Control (NMPC) scheme targeted at motion planning for mechatronic motion systems, such as drones and mobile platforms. NMPC-based motion planning typically requires low computation times to be able to provide control inputs at the required rate for system stability, disturbance rejection, and overall performance. Although there exist various ways in literature to reduce the solution times in NMPC, such times may not be low enough to allow real-time implementations. This paper presents ASAP-MPC, an approach to handle varying, sometimes restrictively large, solution times with an asynchronous update scheme, always allowing for full convergence and real-time execution. The NMPC algorithm is combined with a linear state feedback controller tracking the optimised trajectories for improved robustness against possible disturbances and plant-model mismatch. ASAP-MPC seamlessly merges trajectories, resulting from subsequent NMPC solutions, providing a smooth and continuous overall trajectory for the motion system. This frameworks applicability to embedded applications is shown on two different experiment setups where a state-of-the-art method fails: a quadcopter flying through a cluttered environment in hardware-in-the-loop simulation and a scale model truck-trailer manoeuvring in a structured lab environment.