Real-time Velocity Profile Optimization for Time-Optimal Maneuvering with Generic Acceleration Constraints

2025-09-30

AI Summary

Computing time-optimal velocity profiles under general acceleration constraints remains challenging in robot trajectory planning, as existing methods struggle to balance accuracy and real-time performance. Method: This paper proposes a forward-backward iterative algorithm that optimizes velocity profiles segment-wise along a piecewise-discrete path. It establishes the first unified optimization framework supporting arbitrary acceleration constraints—including non-convex and coupled ones—thereby overcoming the conservatism of conventional box-constrained formulations and the computational inefficiency of high-complexity numerical optimization. The algorithm is robust to discretization resolution and supports user-defined performance bounds and constraint expressions. Results: Evaluated on five tracks and two vehicle platforms, the method achieves trajectory times only 0.11%–0.36% higher than optimal-control benchmarks while accelerating computation by up to three orders of magnitude—enabling online, multi-query real-time deployment.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The computation of time-optimal velocity profiles along prescribed paths, subject to generic acceleration constraints, is a crucial problem in robot trajectory planning, with particular relevance to autonomous racing. However, the existing methods either support arbitrary acceleration constraints at high computational cost or use conservative box constraints for computational efficiency. We propose FBGA, a new underline{F}orward-underline{B}ackward algorithm with underline{G}eneric underline{A}cceleration constraints, which achieves both high accuracy and low computation time. FBGA operates forward and backward passes to maximize the velocity profile in short, discretized path segments, while satisfying user-defined performance limits. Tested on five racetracks and two vehicle classes, FBGA handles complex, non-convex acceleration constraints with custom formulations. Its maneuvers and lap times closely match optimal control baselines (within $0.11%$-$0.36%$), while being up to three orders of magnitude faster. FBGA maintains high accuracy even with coarse discretization, making it well-suited for online multi-query trajectory planning. Our open-source exttt{C++} implementation is available at: https://anonymous.4open.science/r/FB_public_RAL.

Problem

• Optimizing time-optimal velocity profiles under acceleration constraints
• Balancing computational efficiency with generic acceleration constraint handling
• Enabling real-time trajectory planning for autonomous racing applications

Innovation

• Forward-Backward algorithm with generic acceleration constraints
• Maximizes velocity in discretized path segments
• Handles complex non-convex constraints efficiently