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

TL;DR

FBGA introduces a real-time forward-backward algorithm to compute time-optimal velocity profiles along a fixed path under generic g-g-v acceleration envelopes. By discretizing the path into short segments and employing a signed-distance envelope to enforce feasibility, FBGA achieves accuracy comparable to optimal-control benchmarks while delivering up to three orders of magnitude faster computation. The method handles non-convex, speed-dependent acceleration shapes and demonstrates robust performance across diverse track layouts and vehicle types (car and motorcycle). This enables online multi-query trajectory planning and can serve as a fast building block for sampling-based planners in autonomous racing and beyond, with open-source C++ implementation provided.

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 \texttt{C++} implementation is available at: https://anonymous.4open.science/r/FB_public_RAL.

Figures (8)

• Figure 1: (a) Time-optimal velocity and longitudinal acceleration profiles computed by our FBGA along the first two corners of the Catalunya circuit. (b) Lateral acceleration and curvature profiles. Unlike QSS Brayshaw2005, FBGA does not assume that peak lateral accelerations ($a_{y_{\max}}$) occur at curvature peaks ($\kappa_{\max}$): in the second corner, $\kappa_{\max}$ happens between two $a_{y_{\max}}$ peaks.
• Figure 2: (a) g-g-v diagram of the racing motorcycle model Biral2009 used in Section \ref{['sec:results']}. (b) Output of the $D^\pm$ signed distance function (Algorithm \ref{['alg_signed_distance']}) for the red slice in (a). $D^\pm$ ranges from $-1$ (inside the g-g-v envelope) to $+\infty$ (outside). The red line denotes the envelope boundary, where $D^\pm = 0$.
• Figure 3: Main phases of our FBGA, described in Algorithm \ref{['alg_FWBW']}. FBGA takes as input the path (vectors of curvilinear abscissas $\boldsymbol s$ and curvatures $\boldsymbol \kappa$), the initial speed $v_{\mathrm{ini}}$, and the g-g-v acceleration constraints. It outputs vectors with the speed and acceleration profiles $\{\boldsymbol{v}_x, \boldsymbol{a}_x, \boldsymbol{a}_y\}$, and the maneuver time $T$.
• Figure 4: Phases of the FBGA method on an example scenario: maximum speed given the lateral acceleration bounds (top plot), forward pass (center plot, with blue lines when successful), and backward pass (bottom plot, with orange lines when editing invalid forward pass segments).
• Figure 5: Comparison of the MLT-OCP maneuvers for the racing car and motorcycle models of this paper, on the turn n.9 of the Sepang circuit.