Organizations: Delft Center for Systems and Control, Delft University of Technology, Delft, the Netherlands. · School of Mathematics, Southeast University, Nanjing, China. · Department of Advanced Energy, Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277-8561, Japan.
The sudden appearance of a static obstacle on the road, i.e. the moose test, is a well-known emergency scenario in collision avoidance for automated driving. Model Predictive Control (MPC) has long been employed for planning and control of automated vehicles in the state of the art. However, real-time implementation of automated collision avoidance in emergency scenarios such as the moose test remains unaddressed due to the high computational demand of MPC for evasive action in such hazardous scenarios. This paper offers new insights into real-time collision avoidance via the experimental imple- mentation of MPC for motion planning after a sudden and unexpected appearance of a static obstacle. As the state-of-the-art nonlinear MPC shows limited capability to provide an acceptable solution in real-time, we propose a human-like feed-forward planner to assist when the MPC optimization problem is either infeasible or unable to find a suitable solution due to the poor quality of its initial guess. We introduce the concept of maximum steering maneuver to design the feed-forward planner and mimic a human-like reaction after detecting the static obstacle on the road. Real-life experiments are conducted across various speeds and level of emergency using FPEV2-Kanon electric vehicle. Moreover, we demonstrate the effectiveness of our planning strategy via comparison with the state-of- the-art MPC motion planner.
Figures & tables
Figure 1: Elements of the collision avoidance problem after detecting a static obstacle
Figure 2: Single-track vehicle model
Var.
Definition
Units
xego
Global longitudinal position of the CoG
m
yego
Global lateral position of the CoG
m
xobs
Global longitudinal position of the obstacle
m
yobs
Global lateral position of the obstacle
m
vX
Global longitudinal velocity of the CoG
m/s
Table I : List of variables and parameters
Figure 3: The proposed control architecture
Figure 4: Maximum steering maneuver ( 8 ) for different longitudinal velocities.
Figure 5: Sigmoid barrier function examples
Figure 6: Experimental vehicle system configuration.
Parameter
Value
Max iteration
10
Max function evaluation
100
Constraint tolerance
1e-3
Optimality tolerance
1e-3
Step tolerance
1e-3
Table II : Optimization implementation parameters.
Figure 7: Experimental assessment of the τ influence: vehicle trajectory for the desired velocity vx=5 m/s.
Figure 8: Experimental assessment of the ν influence: vehicle trajectory for the desired velocity vx=6 m/s.
Figure 9: Experimental assessment of the hazard: vehicle trajectory for the desired velocity vx=7 m/s.
Figure 10: Comparing the MPC planner in [ 21 ] and our proposed combined planning strategy
Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.
Ricardo Tapia, Iman Soltani
Laboratory for AI, Robotics and Automation, University of California at Davis, Davis, CA 95616 USA
This paper presents a Model Predictive Control-based motion planning and control pipeline for autonomous car racing capable of adapting to different driving contexts, such as overtaking, nominal driving, and countersteering. A Cost Blending state machine manages the identification of different driving contexts and the selection of their predefined weights to be applied to the Model Predictive Planning (MPP) and Control (MPC) modules. The two optimization-based solutions share the same problem formulation and model, differing only in horizon length, rate, tuning, and in their open-loop versus closed-loop approach to maximize the effectiveness of their interaction. The work is validated on the fully autonomous open-wheel racecar Superformula EAV-25, with a lap time achieved that is within 2% of the best human driver reference. The results demonstrate the capability of the solution in driving at the limit of handling, smoothly executing overtaking maneuvers, and quickly reacting to high oversteering conditions to recover the vehicle stability.
Ayoub Raji, Federico Sacco, Nicola Musiu +1
University of Modena and Reggio Emilia, 41125 Modena, Italy · Hipert S.r.l., Modena, Italy
Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited by the need for accurate models and online solution of nonlinear, nonconvex optimization problems in dynamic road environments. Actor-critic reinforcement learning offers a promising alternative for online policy generation, yet its policy-learning process often lacks explicit control-theoretic structure. This article proposes a learning predictive control (LPC) framework with deep Koopman operators for efficient real-time motion planning under nonconvex constraints. To address nonlinear and uncertain vehicle dynamics, a deep-Koopman-based predictor is used to lift the system into an interpretable linear observable space in a data-driven manner. Unlike traditional MPC, which computes open-loop control sequences, the proposed LPC framework yields a closed-loop state-feedback policy within each prediction interval through receding-horizon actor-critic learning. To ensure safety under nonconvex environmental constraints, LPC constructs convex local surrogate representations of obstacles and defines corresponding potential-field functions. These functions and their gradients are directly embedded into the actor-critic structure, enabling efficient, safety-aware policy learning. Extensive simulations and real-world experiments on the HongQi-EHS3 platform demonstrate favorable performance in diverse obstacle-avoidance scenarios in terms of safety, computational efficiency, and driving comfort, compared with benchmark methods such as CBF-MPC and LMPCC.