Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization
🤖 AI Summary
Real-time motion planning for robotic interaction with multi-shape objects requires simultaneous satisfaction of kinematic configuration, collision avoidance, and manipulation behavior constraints—geometric requirements that existing optimization methods struggle to meet efficiently and generally.
Method: We propose ALSPG, a first-order optimization framework that introduces an explicit geometric constraint modeling mechanism integrating Euclidean projection, Minkowski sums, and parameterized basis functions, embedded within an augmented Lagrangian formulation and solved via spectral projected gradient descent.
Contribution/Results: ALSPG unifies unconstrained optimization efficiency with rigorous geometric feasibility guarantees. Evaluated on Franka and P-Rob manipulators and a 1:10-scale vehicle platform, it achieves millisecond-level planning latency—3–5× faster than second-order methods like iLQR—while significantly improving real-time performance, safety, and task accuracy.
Application Category
📝 Abstract
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
Problem
Research questions and friction points this paper is trying to address.
Efficient real-time motion planning for complex robot-object interactions
Overcoming limitations of current optimization solvers in robotics
Leveraging geometric constraints for improved performance in motion generation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses Augmented Lagrangian Spectral Projected Gradient Descent
Leverages geometric projections for efficiency
Improves real-time performance via geometric constraints
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