Topology-Driven Trajectory Optimization for Modelling Controllable Interactions Within Multi-Vehicle Scenario

2025-03-07

AI Summary

Multi-vehicle cooperative trajectory optimization suffers from nonlinearity, non-convexity, and high sensitivity to initial conditions, making vehicle interaction modeling and control challenging. To address this, we introduce topological planning into trajectory optimization—first in the literature—and propose a differentiable local homotopy invariant grounded in differential geometry to characterize dynamic topological relationships among vehicles. We further design differentiable homotopy constraints that enable generation of multiple user-specified, controllable interaction trajectories from a single initial condition. Our method integrates topology-aware nonlinear optimization with a differentiable motion planning framework, ensuring trajectory optimality while significantly improving computational efficiency. Experiments demonstrate superior performance over mainstream baselines in multi-vehicle interaction tasks. The implementation will be open-sourced.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Trajectory optimization in multi-vehicle scenarios faces challenges due to its non-linear, non-convex properties and sensitivity to initial values, making interactions between vehicles difficult to control. In this paper, inspired by topological planning, we propose a differentiable local homotopy invariant metric to model the interactions. By incorporating this topological metric as a constraint into multi-vehicle trajectory optimization, our framework is capable of generating multiple interactive trajectories from the same initial values, achieving controllable interactions as well as supporting user-designed interaction patterns. Extensive experiments demonstrate its superior optimality and efficiency over existing methods. We will release open-source code to advance relative research.

Problem

• Optimize trajectories in multi-vehicle scenarios with non-linear, non-convex challenges.
• Model controllable interactions using a differentiable local homotopy invariant metric.
• Generate multiple interactive trajectories from same initial values with user-designed patterns.

Innovation

• Differentiable local homotopy invariant metric
• Topological metric as optimization constraint
• Generates multiple interactive trajectories