-- 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 hyper-planes 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. Deploying autonomous robots in practical and real-life settings, e.g., a warehouse, industrial production cell, homes, etc. is a complex problem with many interesting challenges that remain.

We consider the challenge of black-box optimization within hybrid discrete-continuous and variable-length spaces, a problem that arises in various applications, such as decision tree learning and symbolic regression. We propose DisCo-DSO (Discrete-Continuous Deep Symbolic Optimization), a novel approach that uses a generative model to learn a joint distribution over discrete and continuous design variables to sample new hybrid designs. In contrast to standard decoupled approaches, in which the discrete and continuous variables are optimized separately, our joint optimization approach uses fewer objective function evaluations, is robust against non-differentiable objectives, and learns from prior samples to guide the search, leading to significant improvement in performance and sample efficiency. Our experiments on a diverse set of optimization tasks demonstrate that the advantages of DisCo-DSO become increasingly evident as the complexity of the problem increases. In particular, we illustrate DisCo-DSO's superiority over the state-of-the-art methods for interpretable reinforcement learning with decision trees.

The aim of coordinated planning is to avoid robot-to-robot collisions in a multi-robot system, and there are two standard solution approaches: centralized planning and decoupled planning. Our first contribution is a decoupled planning approach that ensures C2-continuous control commands with zero velocities at the start and goal. We benchmark our decoupled approach with a centralized approach. Contrary to literature, we show that for a standard motion planning pipeline, such as the one used by MoveIt!, centralized planning is superior to decoupled planning in dual-arm manipulation: It has a lower computation time and a higher robustness. Our second contribution is an optimization that minimizes the rotational motion of an end-effector while considering obstacle avoidance. We derive the analytic gradients of this optimization problem, making the algorithm suitable for online motion planning. Our optimization extends an existing path quality improvement method. Integrating it into our decoupled approach overcomes its shortcomings and provides a motion planning pipeline that is robust at up to 99.9% with a planning time of less than 1s and that computes high-quality paths.