Motion planning around obstacles with convex optimization.

Area of Science:

• Robotics
• Optimization
• Motion Planning

Background:

• Motion planning around obstacles is crucial for robots in diverse applications.
• Optimization-based planners struggle with nonconvexity in cluttered environments.
• Sampling-based planners have limitations in high dimensions and with differential constraints.

Purpose of the Study:

• To develop a framework enabling convex optimization for efficient and reliable obstacle-free motion planning.
• To address limitations of existing planning methods in complex, high-dimensional spaces.

Main Methods:

• Developed a practical convex relaxation of the motion planning problem using Graphs of Convex Sets (GCS).
• Utilized recent techniques for shortest path finding within GCS.
• Applied a cost-effective postprocessing step to the relaxed solution.

Main Results:

• The convex relaxation is typically very tight, yielding near-globally optimal collision-free trajectories.
• The GCS planner finds better trajectories in less time compared to sampling-based algorithms.
• Demonstrated reliable trajectory design in high-dimensional, complex environments through simulations and hardware experiments.

Conclusions:

• The GCS framework offers a significant advancement in robotic motion planning, particularly for cluttered environments.
• Convex optimization can be effectively applied to motion planning problems with complex constraints.
• The proposed method provides a more efficient and reliable alternative to traditional sampling-based approaches.