Full-state nonlinear trajectory tracking control of underactuated surface vessels

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1286-1296 ◽  
Author(s):  
Karl L Fetzer ◽  
Sergey Nersesov ◽  
Hashem Ashrafiuon
Keyword(s):  
Trajectory Tracking ◽  
Sliding Mode ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Control Approach ◽  
Surface Vessels ◽  
Modeling Uncertainties ◽  
Underactuated Surface Vessels ◽  
System States ◽  
Error Dynamics

This article presents the development, implementation, and comparison of two trajectory tracking nonlinear controllers for underactuated surface vessels. A control approach capable of stabilizing all the states of any planar vehicle is specifically adapted to surface vessels. The method relies on transformation of the six position and velocity state dynamics into a four-state error dynamics. The backstepping and sliding mode control laws are then derived for stabilization of the error dynamics and proven to stabilize all system states. Simulations are presented in the absence and presence of modeling uncertainties and unknown disturbances. An experimental setup is then described, followed by successful experimental implementation and comparison of the two controllers.

Modeling and trajectory tracking control of a two-wheeled mobile robot: Gibbs–Appell and prediction-based approaches

Robotica ◽  
2018 ◽  
Vol 36 (10) ◽  
pp. 1551-1570 ◽  
Author(s):  
Hossein Mirzaeinejad ◽  
Ali Mohammad Shafei
Keyword(s):  
Trajectory Tracking ◽  
Dynamic Models ◽  
Sliding Mode ◽  
Tracking Accuracy ◽  
Wheeled Mobile Robots ◽  
Tracking Errors ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Control Approach ◽  
Prediction Time

SUMMARYThis study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

Formation Control for Underactuated Surface Vessel Networks

2020 ◽  
Author(s):  
Bo Wang ◽  
Sergey Nersesov ◽  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Model ◽  
Formation Control ◽  
Sliding Mode ◽  
Nonlinear Dynamical System ◽  
Order Error ◽  
Reduced Order ◽  
Control Approach ◽  
Surface Vessels ◽  
Underactuated Surface Vessels ◽  
Error Dynamics

Abstract Developing distributed control algorithms for multi-agent systems is difficult when each agent is modeled as a nonlinear dynamical system. Moreover, the problem becomes far more complex if the agents do not have sufficient number of actuators to track any arbitrary trajectory. In this paper, we present the first fully decentralized approach to formation control for networks of underactuated surface vessels. The vessels are modeled as three degree of freedom planar rigid bodies with two actuators. Algebraic graph theory is used to model the network as a directed graph and employing a leader-follower model. We take advantage of the cascade structure of the combined nonlinear kinematic and dynamic model of surface vessels and develop a reduced-order error dynamic model using a state transformation definition. The error dynamics and consequently all system states are then stabilized using sliding mode control approach. It is shown that the stabilization of the reduced-order error dynamics guarantees uniform global asymptotic stability of the closed-loop system subject to bounded uncertainties. The proposed control method can be implemented in directed time-invariant communication networks without the availability of global position measurements for any of the vehicles participating in the network. An example of a a network of five surface vessels is simulated to verify the effective performance of the proposed control approach.

Trajectory Tracking of Underactuated Surface Vessels Based on Hierarchical Sliding Mode

2014 ◽  
Author(s):  
Cheng Liu ◽  
Zaojian Zou ◽  
Jianchuan Yin
Keyword(s):  
Trajectory Tracking ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Underactuated System ◽  
Sliding Mode Controller ◽  
Control Field ◽  
Surface Vessels ◽  
Underactuated Surface Vessels ◽  
Hierarchical Sliding Mode

Trajectory tracking is an importance practice in ship motion control field. It attracts more attention recently due to its difficulties. Trajectory tracking requires the ship to arrive pinpoint location at exact time. It is a underactuated system because the degrees of freedom of control inputs are fewer than the degrees of freedom that needed to be controlled. In this paper, a hierarchical sliding mode controller and a common sliding mode controller are proposed to deal with the trajectory tracking problem of underactuated surface vessels. Simulation results validate the tracking performance of the proposed controllers. The closed-loop stability is testified by the Lyapunov stability theorem.

scholarly journals Trajectory Tracking Control for Underactuated USV with Prescribed Performance and Input Quantization

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2208
Author(s):  
Kunyi Jiang ◽  
Lei Mao ◽  
Yumin Su ◽  
Yuxin Zheng
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Mapping Function ◽  
Trajectory Tracking Control ◽  
Prescribed Performance ◽  
Input Quantization ◽  
Performance Requirements ◽  
Radial Basis Neural Networks ◽  
Surface Vessels ◽  
Error Dynamics

This paper is devoted to the problem of prescribed performance trajectory tracking control for symmetrical underactuated unmanned surface vessels (USVs) in the presence of model uncertainties and input quantization. By combining backstepping filter mechanisms and adaptive algorithms, two robust control architectures are investigated for surge motion and yaw motion. To guarantee the prespecified performance requirements for position tracking control, the constrained error dynamics are transformed to unconstrained ones by virtue of a tangent-type nonlinear mapping function. On the other hand, the inaccurate model can be identified through radial basis neural networks (RBFNNs), where the minimum learning parameter (MLP) algorithm is employed with a low computational complexity. Furthermore, quantization errors can be effectively reduced even when the parameters of the quantizer remain unavailable to designers. Finally, the effectiveness of the proposed controllers is verified via theoretical analyses and numerical simulations.

PD-Based Trajectory Tracking Control for Robot Manipulators

1993 ◽  
Vol 115 (3) ◽  
pp. 566-569 ◽  
Author(s):  
Cao Bailin ◽  
Chen Huitang
Keyword(s):  
Trajectory Tracking ◽  
Sliding Mode ◽  
Tracking System ◽  
Coefficient Matrix ◽  
Trajectory Tracking Control ◽  
Control Laws ◽  
Globally Asymptotically Stable ◽  
Control Scheme ◽  
Frictional Forces ◽  
Globally Stable

In this paper, it is proved that a trajectory tracking system of a manipulator is globally stable if the system is controlled under the decentralized PD control law plus a sliding term with a constant coefficient, and the norm of the coefficient matrix of its differential term is no less than that of the centripetal and Coriolis’ force term corresponding to the desired angular velocity, i.e., ∥Kd∥ ≥ ∥C(q, q˙d)∥. Condition ∥Kd∥ ≥ ∥C(q, q˙d)∥ implies that Kd increases only with q˙d instead of q˙. A type of globally asymptotically stable adaptive sliding mode PD-based control scheme is proposed, and the proof of stability of the system is also given. It is easy to implement in real-time compared with other adaptive control laws as no estimation of gravitational and frictional forces is necessary.

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