Ensuring Feasibility and Safety in Constrained Optimal Control of Heterogeneous Vehicle Platoons

Core Concepts

This paper proposes a new type of control barrier function (CBF) to guarantee the feasibility of quadratic programs (QPs) used in safety-critical control, while satisfying safety requirements. The method is demonstrated on an adaptive cruise control problem for a heterogeneous vehicle platoon with tight control bounds.

Abstract

The paper studies safety and feasibility guarantees for systems with tight control bounds. It has been shown that stabilizing an affine control system while optimizing a quadratic cost and satisfying state and control constraints can be mapped to a sequence of QPs using control barrier functions (CBFs) and control Lyapunov functions (CLFs).
One of the main challenges is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds. The authors define a feasibility constraint and propose a new type of CBF to enforce it. This guarantees the feasibility of the QPs, while satisfying safety requirements.
The proposed method is demonstrated on an Adaptive Cruise Control (ACC) problem for a heterogeneous platoon with tight control bounds. The results show that the proposed approach can generate gradually transitioned control (without abrupt changes) with guaranteed feasibility and safety, outperforming existing CBF-CLF approaches.

Stats

The vehicle dynamics are described by the following equations:
˙xj(t) = [vj(t), -1/Mj Fr(vj(t))]^T
˙vj(t) = [0, 1/Mj]^T uj(t)
where Mj is the mass of the jth vehicle, vj(t) is the velocity, xj(t) is the position, and uj(t) is the acceleration (control input).
The resistance force Fr(vj(t)) = f0 sgn(vj(t)) + f1 vj(t) + f2 vj^2(t), with f0, f1, f2 as positive scalars.

Quotes

"One of the main challenges in this method is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds."
"We define a feasibility constraint and propose a new type of CBF to enforce it. Our method guarantees the feasibility of the above mentioned QPs, while satisfying safety requirements."

Key Insights Distilled From

Feasibility-Guaranteed Safety-Critical Control with Applications to Heterogeneous Platoons

by Shuo Liu,Wei... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2310.00238.pdf

Deeper Inquiries

How can the proposed method be extended to handle additional hard constraints beyond safety and control bounds, such as energy consumption or passenger comfort

The proposed method can be extended to handle additional hard constraints beyond safety and control bounds by incorporating them into the optimization framework as additional constraints. For constraints related to energy consumption, an objective function term can be added to the cost function to minimize energy usage while satisfying safety and feasibility constraints. This additional term would introduce a trade-off between safety, feasibility, and energy efficiency in the optimization problem.
Similarly, for constraints related to passenger comfort, variables representing comfort metrics can be included in the optimization problem. These variables can be optimized to ensure passenger comfort while maintaining safety and feasibility. By formulating these constraints as part of the optimization problem, the proposed method can handle a wider range of requirements beyond safety and control bounds.

What are the potential limitations of the auxiliary-function based CBF approach, and how could it be further generalized to handle a wider range of safety-critical control problems

The potential limitations of the auxiliary-function based CBF approach include the complexity of defining the auxiliary functions and ensuring their effectiveness in enforcing feasibility constraints. The method may also face challenges in scenarios where there are conflicting constraints or when the system dynamics are highly nonlinear.
To further generalize the approach, one possible direction is to explore adaptive or learning-based techniques to dynamically adjust the auxiliary functions based on real-time system behavior. This adaptive approach could enhance the method's adaptability to changing conditions and improve its performance in handling a wider range of safety-critical control problems.
Additionally, incorporating robust optimization techniques or integrating probabilistic methods to account for uncertainties in the system could enhance the method's robustness and applicability to diverse scenarios. By addressing these limitations and exploring advanced optimization strategies, the auxiliary-function based CBF approach can be further generalized to handle complex safety-critical control problems effectively.

How could the insights from this work on feasibility-guaranteed safety-critical control be applied to other domains beyond vehicle platoons, such as robotics or aerospace systems

The insights from this work on feasibility-guaranteed safety-critical control can be applied to other domains beyond vehicle platoons, such as robotics or aerospace systems, by adapting the methodology to the specific requirements of these domains. In robotics, the approach can be used to ensure safe and feasible motion planning for robotic systems operating in dynamic environments. By defining appropriate safety constraints and feasibility criteria, the method can enable robots to navigate complex environments while avoiding collisions and maintaining operational constraints.
In aerospace systems, the insights can be leveraged to design control strategies for aircraft or spacecraft that prioritize safety and feasibility. By incorporating constraints related to flight dynamics, fuel efficiency, and system limitations, the method can be tailored to optimize the performance of aerospace systems while ensuring safe and reliable operation. The application of feasibility-guaranteed safety-critical control principles in these domains can enhance the overall reliability and efficiency of autonomous systems.