Trajectory Planning Using Safe Ellipsoidal Corridors as Projections of Orthogonal Trust Regions

2025-09-23

AI Summary

Efficient and smooth collision-free trajectory planning in complex environments remains a fundamental challenge in robotics. Existing corridor-based approaches are constrained by the quality of free-space decomposition and explicit time allocation, limiting their scalability to highly geometrically complex scenes. This paper introduces the Orthogonal Trust Region Planning (Orth-TRP) framework, which parameterizes trajectories as the Cartesian product of orthogonal trust regions. Ellipsoidal safety corridors implicitly encode spatiotemporal constraints, eliminating the need for explicit time parametrization. By leveraging convex relaxation and separable block-wise constraints, Orth-TRP decouples problem dimensionality from environmental complexity, enabling parallel optimization. Evaluated on quadrotor benchmark tasks, Orth-TRP achieves significantly reduced computation time while generating smoother, safer trajectories—outperforming state-of-the-art corridor methods, especially in highly cluttered environments.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental complexity and require explicit allocations of time windows to trajectory segments. We introduce a new trajectory parameterization that represents trajectories in a nonconvex collision free corridor as being in a convex cartesian product of balls. This parameterization allows us to decouple problem size from geometric complexity of the solution and naturally avoids explicit time allocation by allowing trajectories to evolve continuously inside ellipsoidal corridors. Building on this representation, we formulate the Orthogonal Trust Region Problem (Orth-TRP), a specialized convex program with separable block constraints, and develop a solver that exploits this parallel structure and the unique structure of each parallel subproblem for efficient optimization. Experiments on a quadrotor trajectory planning benchmark show that our approach produces smoother trajectories and lower runtimes than state-of-the-art corridor based planners, especially in highly complicated environments.

Problem

• Planning collision-free robot trajectories in complex environments
• Overcoming poor scalability of existing corridor-based planners
• Avoiding explicit time allocation for trajectory segments

Innovation

• Parameterizes trajectories as convex cartesian product of balls
• Formulates Orthogonal Trust Region Problem with separable constraints
• Develops parallel solver exploiting unique subproblem structures