A Computationally Efficient Framework for Free-trajectory Minimum-lap-time Optimization of Racing Cars

TL;DR

The paper addresses minimum-time lap optimization for racing cars by jointly optimizing the racing line and powertrain operation. It introduces a sequential-convex programming (SCP) framework built on a second-order cone program (SOCP) that linearizes nonconvex constraints around previous iterates, enabling fast convergence. The approach preserves convexity for most model components, achieves solving times of a few seconds per iteration and typically 4 iterations to reach a sub-2 hundredth of a second lap-time improvement, and shows a ~4% lap-time gain over a minimum-curvature baseline while validating energy-management compatibility. These results suggest the method is suitable for real-time control and energy management in racing applications, and confirm that energy limitations rarely alter the optimal racing line in typical use cases.

Abstract

This paper presents a modeling and optimization framework to compute the minimum-lap-time spatial trajectory and powertrain operation of racing cars in a computationally efficient fashion. Specifically, we first derive a quasi-steady-state model of a racing car, whereby the racing line trajectory is jointly optimized. Next, we frame the minimum-lap-time problem and leverage its mostly convex structure by devising a sequential convex programming solution algorithm. We benchmark our method against off-the-shelf nonlinear programming solvers, showing how it can bring computation time down from a few minutes to a few seconds, paving the way for real-time implementations. Moreover, we compare our results to similarly efficient minimum-curvature racing line optimization methods, showing how a minimum-time-based racing line might lead to 4% faster lap-times. Finally, we showcase our framework for optimal powertrain energy management and we validate the common modeling assumption that the racing line is unaffected by energy limitations, showing that this assumption results in marginal lap-time losses of under 0.1%.

Figures (11)

• Figure 1: Optimal racing line and speed trajectory over the Interlagos Circuit.
• Figure 2: 3D-ribbon track model, defined by a central trajectory and a normal vector. Positions on the track are defined by an offset along this vector.
• Figure 3: Top, side and frontal view of the simulated model. The forces acting on the vehicle are highlighted. The arrows indicate positive force directions.
• Figure 4: Tire grip envelope of the proposed load-dependent grip coefficients model compared to the simpler model with fixed coefficients and the high-fidelity Magic Formula tire model. Our proposed implementation reduces the normalized root-mean-square error by a factor of 10.
• Figure 5: Origins of the tire cornering resistance. No lateral force is possible without a tire slip angle, and the slip angle creates a force component opposing the direction of motion.