Search arXivSearch

arXiv · 2206.04264

Formation Tracking for a Multi-Auv System Based on an Adaptive Sliding Mode Method in the Water Flow Environment

Abstract

In this paper, formation tracking for a multi-AUV system (MAS) using an improved adaptive sliding mode control method is studied in the Three Dimensional (3-D) underwater environment. Firstly, the kinematics model and the dynamic model of the AUVs are given as the Six Dimensions of Freedom (6-DOF) considered. Then, control law based on the mathematical model of the AUVs is proposed based on the improved sliding mode method. A second order sliding mode control method is adopted to eliminate the chatting phenomenon of the controller. Thirdly, considering the water flow in the underwater working environment of the AUVs, an adaptive module is added to the controller. With the adaptive approach, the finite disturbances caused by water flow could be handled with the controller. The proposed method achieves stability by substituting an adaptive continuous term for the switching term in the controller. At last, a robust sliding mode controller with continuous model predictive control strategy for the multi-AUV system is developed to achieve leader-follower formation tracking under the presence of bounded flow disturbances, and simulations are implemented to confirm the effectiveness of the proposed method.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xin Li, Daqi Zhu, Bing Sun, Qi Chen, Wenyang Gan, Zhigang Li. 2023-01-17. Formation Tracking for a Multi-Auv System Based on an Adaptive Sliding Mode Method in the Water Flow Environment. https://arxiv.org/abs/2206.04264

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY