Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization

Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc

GP-enhanced Autonomous Drifting Framework using ADMM-based iLQR

Autonomous drifting is a complex challenge due to the highly nonlinear dynamics and the need for precise real-time control, especially in uncertain environments. To address these limitations, this paper presents a hierarchical control framework for autonomous vehicles drifting along general paths, primarily focusing on addressing model inaccuracies and mitigating computational challenges in real-time control. The framework integrates Gaussian Process (GP) regression with an Alternating Direction Method of Multipliers (ADMM)-based iterative Linear Quadratic Regulator (iLQR). GP regression effectively compensates for model residuals, improving accuracy in dynamic conditions. ADMM-based iLQR not only combines the rapid trajectory optimization of iLQR but also utilizes ADMM's strength in decomposing the problem into simpler sub-problems. Simulation results demonstrate the effectiveness of the proposed framework, with significant improvements in both drift trajectory tracking and computational efficiency. Our approach resulted in a 38$\%$ reduction in RMSE lateral error and achieved an average computation time that is 75$\%$ lower than that of the Interior Point OPTimizer (IPOPT).