ABSTRACT This paper tackles vehicle tracking and obstacle avoidance by integrating path planning into a model‐ and data‐driven predictive control framework using Gaussian processes (GP‐MDPC) and backoffs. Autonomous driving is inherently uncertain and stochastic, making vehicle tracking with obstacle avoidance a stochastic constrained control problem best addressed by stochastic nonlinear model predictive control (SNMPC). The proposed GP‐MDPC approach offers two key advantages over the current state‐of‐the‐art SNMPC. Firstly, GPs learn unknown dynamics from measurements, the predictions and uncertainty quantification generated by GPs are subsequently propagated through the nominal vehicle model for updating state mean and covariance equations. Besides, sparse GPs replace full GPs to reduce computational demand and speed up online evaluation. Secondly, a backoff approximation method is explored to reformulate the chance constraints into tractable expressions by tuning backoffs offline from generated closed‐loop Monte Carlo samples. This method resolves the tradeoff between robustness and the risk of constraint violation, as well as guarantees online recursive feasibility. Compared to Chebyshev's inequality method, the backoff approach alleviates the conservatism caused by chance constraint approximation and thus improves vehicle tracking performance. The geometric relationship between the vehicle and obstacles is converted into chance constraints, which, together with the evolution equations for the state mean and covariance, are combined to formulate a finite‐horizon stochastic optimal control problem. Simulations demonstrate that the sparse GP‐MDPC using backoffs is more preferred than the full GP‐MDPC either using backoffs or Chebyshev's inequality by improving computational efficiency while maintaining satisfactory tracking performance as well as safety.
Xie et al. (2026) studied this question.