Key Takeaways & Executive Findings
- •• Extends robust control invariant (RCI) tubes to motion planning, enabling preemptive handling of closed-loop uncertainties. • Translates state and control constraints into RCI tube constraints, ensuring safety and optimality beyond nominal open-loop models. • Introduces a parameterized explicit iterative expression for ellipsoidal uncertainty propagation, accelerating the solving process. • Validates the framework under kinematic and dynamic vehicle models with various uncertainties, demonstrating fast, closed-loop safety and robustness.
Abstract
This paper tackles uncertainties between planning and actual models. It extends the concept of RCI (robust control invariant) tubes, originally a parameterized representation of closed-loop control robustness in traditional feedback control, to the domain of motion planning for autonomous vehicles. Thus, closed-loop system uncertainty can be preemptively addressed during vehicle motion planning. This involves selecting collision-free trajectories to minimize the volume of robust invariant tubes. Furthermore, constraints on state and control variables are translated into constraints on the RCI tubes of the closed-loop system, ensuring that motion planning produces a safe and optimal trajectory while maintaining flexibility, rather than solely optimizing for the open-loop nominal model. Additionally, to expedite the solving process, we were inspired by L2 gain to parameterize the RCI tubes and developed a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets within closed-loop systems. Furthermore, we applied the pseudospectral orthogonal collocation method to parameterize the optimization problem of transcribing trajectories using high-order Lagrangian polynomials. Finally, under various operating conditions, we incorporate both the kinematic and dynamic models of the vehicle and also conduct simulations and analyses of uncertainties such as heading angle measurement, chassis response, and steering hysteresis. Our proposed robust motion planning framework has been validated to effectively address nearly all bounded uncertainties while anticipating potential tracking errors in control during the planning phase. This ensures fast, closed-loop safety and robustness in vehicle motion planning.
1. Introduction
Autonomous vehicle navigation typically involves three main components: perception, planning, and control. In the planning phase, smooth curves or simplified models (e.g., kinematics model, 2-DoF dynamics models) are commonly employed to determine the trajectory to be followed and the corresponding nominal feedforward inputs for the control system. Through collaborative efforts between academia and industry, considerable advancements have been achieved in autonomous motion planning for vehicles, particularly in addressing challenges such as non-convex obstacle avoidance constraints, nonlinear dynamics, and other related aspects. However, devising a completely safe and optimal trajectory for closed-loop vehicle systems with uncertain nonlinear and underactuated dynamics remains a significant challenge.
The primary issue arises from two main factors: (1) Vehicle motion planning typically targets nominal systems ˙x = f (x, u), overlooking disturbances present in real physical systems, including variations in system parameters and states. As vehicle speed and lateral acceleration increase, unmodeled dynamics are further exacerbated, denoted as ˙x = f (x, u, w). Relying solely on planning for nominal models inevitably leads to tracking errors that cannot be anticipated in advance, posing a critical threat to the safety of autonomous vehicle operations. As shown in Figure 1, the black dashed line denotes the nominal planned trajectory, which doesn’t consider uncertainty. Meanwhile, the blue area illustrates the potential error range of the control layer tracking the nominal trajectory over time, influenced by uncertainty (Cross sections of RCI tubes in x and y coordinate systems). The light orange shadow delineates the swept area of the vehicle’s outer contour within the tracking error range. This observation suggests that the closed-loop behavior resulting from tracking the nominal planning trajectory under uncertainty is prone to being unsafe. (2) Autonomous vehicle motion planning often considers detailed metrics such as minimum jerk and personalized driving. While these metrics may realize fine-grained planning in nominal models, they can detrimentally affect closed-loop trajectory tracking performance. In extreme cases, conflicting requirements between open-loop optimality and closed-loop safety may conflict, leading to unsafe outcomes.
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Mingzhuo Zhao, Tong Shen, Fanxun Wang, Guodong Yin (2025). Fast, Safe and Robust Motion Planning for Autonomous Vehicles Based on Robust Control Invariant Tubes. Chinese Journal of Mechanical Engineering. https://doi.org/10.1186/s10033-025-01216-8
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Frequently Asked Questions
What is the main contribution of this paper?
The paper extends robust control invariant (RCI) tubes to motion planning for autonomous vehicles, enabling preemptive handling of closed-loop uncertainties and ensuring safety and robustness.
How does the proposed framework handle uncertainties?
It translates state and control constraints into constraints on RCI tubes of the closed-loop system, and uses a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets, allowing anticipation of tracking errors during planning.
What methods are used to expedite the solving process?
The authors use L2 gain to parameterize RCI tubes and apply the pseudospectral orthogonal collocation method to transcribe trajectories using high-order Lagrangian polynomials.
What models and uncertainties are considered in validation?
Both kinematic and dynamic vehicle models are incorporated, and uncertainties such as heading angle measurement, chassis response, and steering hysteresis are analyzed under various operating conditions.
What is the significance of this work for autonomous driving?
The framework ensures fast, closed-loop safety and robustness in vehicle motion planning, addressing nearly all bounded uncertainties and improving reliability in real-world scenarios.
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