Immersion and invariance vs sliding mode control for reference trajectory tracking of autonomous vehicles

Tagne, Gilles; Talj, Reine; Charara, Ali · 2014 · Crossref

DOI: 10.1109/ecc.2014.6862436

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Summary

This paper addresses the lateral control problem for autonomous vehicles, specifically focusing on minimizing lateral displacement relative to a reference trajectory. Motivated by the need for robust control strategies capable of handling vehicle nonlinearities and environmental disturbances, the authors compare two distinct control approaches: Higher-Order Sliding Mode Control (SMC) and Immersion and Invariance (I&I) control. While SMC is recognized for its robustness against uncertainties, it suffers from chattering. The I&I approach, a newer method for nonlinear control, offers a theoretical framework that implicitly resembles SMC but allows for stronger stability guarantees. The study aims to highlight the advantages and disadvantages of each strategy for robust lane-keeping applications. The methodology involves designing controllers based on a linear parameter-varying bicycle model, where longitudinal velocity is treated as a varying parameter. The state vector includes sideslip angle, yaw rate, lateral error, and its derivative. For the SMC controller, a super-twisting algorithm is employed to minimize chattering, utilizing a sliding variable defined by lateral error and its derivative. The I&I controller is designed by immersing the plant dynamics into a lower-order target system that captures the desired behavior, rendering a specific manifold invariant and attractive. Both controllers use the same sensor signals, including sideslip angle and yaw rate. Validation was conducted via closed-loop simulations in Matlab-Simulink using experimental data acquired from the DYNA vehicle (a Peugeot 308) at the CERAM testing center. The simulations incorporated a more representative four-wheel vehicle model with Dugoff’s tire model to ensure realistic validation under various driving scenarios. The results demonstrate that both control strategies effectively minimize lateral displacement and exhibit robustness against disturbances. However, the I&I controller provides distinct advantages. Theoretically, the I&I approach guarantees global asymptotic stability for all positive controller gains, a stronger criterion than the finite-time convergence of SMC. Furthermore, the response time of the I&I controller is explicitly determined by its design parameters, allowing for predictable performance tuning. In contrast, SMC performance is more sensitive to gain selection and parameter uncertainties, such as variations in tire cornering stiffness. The simulations confirm that the I&I controller maintains stability and performance even when vehicle parameters like mass or cornering stiffness vary, whereas the SMC controller shows greater sensitivity to these uncertainties. The significance of this work lies in providing a comparative analysis of two robust control techniques for autonomous vehicle lateral guidance. It highlights that while SMC is effective, the I&I principle offers superior structural properties, including guaranteed stability for any positive gains and tunable response times. This makes I&I a promising candidate for adaptive and nonlinear control applications in automotive systems, where robustness and predictable performance are critical. The study contributes to the field by offering a rigorous theoretical and experimental comparison, aiding in the selection of appropriate control strategies for advanced driver assistance systems.

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