DRCC-LPVMPC: Robust Data-Driven Control for Autonomous Driving and Obstacle Avoidance

Abstract

Safety in obstacle avoidance is critical for autonomous driving. While model predictive control (MPC) is widely used, simplified prediction models such as linearized or single-track vehicle models introduce discrepancies between predicted and actual behavior that can compromise safety. This paper proposes a distributionally robust chance-constrained linear parameter-varying MPC (DRCC-LPVMPC) framework that explicitly accounts for such discrepancies. The single-track vehicle dynamics are represented in a quasi-linear parameter-varying (quasi-LPV) form, with model mismatches treated as additive uncertainties of unknown distribution. By constructing chance constraints from finite sampled data and employing a Wasserstein ambiguity set, the proposed method avoids restrictive assumptions on boundedness or Gaussian distributions. The resulting DRCC problem is reformulated as tractable convex constraints and solved in real time using a quadratic programming solver. Recursive feasibility of the approach is formally established. Simulation and real-world experiments demonstrate that DRCC-LPVMPC maintains safer obstacle clearance and more reliable tracking than conventional nonlinear MPC and LPVMPC controllers under significant uncertainties.

Figures (13)

• Figure 1: Overview of the derivation and design process of DRCC-LPVMPC, highlighting the transition from the nonlinear vehicle model to the quasi-LPV representation with additive uncertainties, and the formulation of the chance-constrained problem using the right-hand CVaR constraint.
• Figure 2: Safety region defined in the TNB frame and converted back to the Cartesian frame.
• Figure 3: Tangent line of the obstacle avoidance constraints at time steps $i$ and $j$, where $h_i$ and $h_j$ represent the safe region boundary tangent lines at $[x^\text{ref}_i,y^\text{ref}_i]$ and $[x^\text{ref}_j,y^\text{ref}_j]$, respectively.
• Figure 4: Depiction of CVaR for a function with an unknown distribution (illustrated as Gaussian for convenience). The Value-at-Risk (VaR) represents the threshold below which a specified percentage ($\epsilon$) of the distribution lies, while CVaR accounts for the average loss beyond this threshold, effectively capturing tail risk. The shaded region accounts for $\epsilon \times 100\%$ of the mass of the unknown distribution.
• Figure 5: Summary of the conversion process from infinite-dimensional DRCC to convex constraints using a data-driven approach.

Theorems & Definitions (11)

• Theorem 1
• proof
• Theorem 2
• proof
• Corollary 1
• proof
• Remark 1
• Remark 2
• Theorem 3
• proof