Velocity prediction and planning based on tire force saturation coefficients for autonomous vehicle under RS curve path

Reeds–Shepp (RS) curves are widely employed for path smoothing in path planning algorithms such as Hybrid A* and Rapidly-Exploring Random Trees (RRT). To ensure the stability of autonomous vehicles when traversing RS-curve paths, this paper proposes a velocity prediction and planning algorithm based on vehicle lateral dynamics. Specifically, given the path curvature and initial velocity, the yaw rate and side-slip angle of the vehicle during steady-state steering are derived using the lateral dynamics model. Considering load transfer effects, the lateral tire force is calculated from the rate of change of vertical loads, and the safe driving velocity is predicted through gradient descent with the tire force saturation coefficient as the optimization objective. Subsequently, a velocity planning method that integrates the Gaussian pseudospectral method (GPM) with sequential quadratic programming (SQP) is developed. The problem is formulated as a nonlinear programming model, in which the predicted safe velocity serves as the upper velocity constraint. Joint simulations in MATLAB/Simulink and CarSim are then conducted to evaluate the proposed framework. The results show that the prediction accuracy of the lateral tire force exceeds 94% under different road friction coefficients, confirming the reliability of the proposed prediction model. Furthermore, comparative experiments demonstrate that the velocity planning method can effectively reduce vehicle velocity from unsafe to safe levels, thereby ensuring driving stability and safety when negotiating curves.