Set-Theoretic Receding Horizon Control for Obstacle Avoidance and Overtaking in Autonomous Highway Driving

Abstract

This article addresses obstacle avoidance motion planning for autonomous vehicles, specifically focusing on highway overtaking maneuvers. The control design challenge is handled by considering a mathematical vehicle model that captures both lateral and longitudinal dynamics. Unlike existing numerical optimization methods that suffer from significant online computational overhead, this work extends the state-of-the-art by leveraging a fast set-theoretic ellipsoidal Model Predictive Control (Fast-MPC) technique. While originally restricted to stabilization tasks, the proposed framework is successfully adapted to handle motion planning for vehicles modeled as uncertain polytopic discrete-time linear systems. The control action is computed online via a set-membership evaluation against a structured sequence of nested inner ellipsoidal approximations of the exact one-step ahead controllable set within a receding horizon framework. A six-degrees-of-freedom (6-DOF) nonlinear model characterizes the vehicle dynamics, while a polytopic embedding approximates the nonlinearities within a linear framework with parameter uncertainties. Finally, to assess performance and real-time feasibility, comparative co-simulations against a baseline Non-Linear MPC (NLMPC) were conducted. Using the high-fidelity CARLA 3D simulator, results demonstrate that the proposed approach seamlessly rejects dynamic traffic disturbances while reducing online computational time by over 90% compared to standard optimization-based approaches.

Figures (25)

• Figure 1: Overtaking maneuver: the autonomous (ego) vehicle executes a lane change (i) to overtake the preceding (lead) vehicle (ii). After successfully passing the lead vehicle, the ego vehicle either returns to its original lane (iii.a) or continues in the new lane if necessary (iii.b), depending on traffic conditions. (X,Y) global reference frame
• Figure 2: Way-points ($\mathcal{W} = \left[w_1,\ldots,w_6\right]$ (red trajectory) describing a feasible paths; way-points $\mathcal{W}' = \left[w_7,\ldots,w_6\right]$ (blue trajectory) describing an alternative feasible paths; points ($\mathcal{W}_{1} = \left[w_{1}^1,\ldots,w_{1}^4\right]$; $\mathcal{W}_{2} = \left[w_{2}^1,\ldots,w_{2}^4\right]$) describing the obstacle scenario $\mathcal{O}=\left\{Ob_1,Ob_2\right\}$.
• Figure 3: Sequence of ellipsoidal inner approximations construction.
• Figure 4: Full path generation: ellipsoid set $\mathcal{E}_i^s$ sequence (white ellipsoid) generated in response to the presence of the vehicle $Ob_1$, updated ellipsoid set $\mathcal{E}_i^s$ sequence (green ellipsoid) accounting the new vehicle $Ob_2$, final path (red arrows).
• Figure 5: Vehicle Dynamic Model (a), Wheel Dynamic Model (b) and Slip Angle $\alpha$ (c).