Underactuated Vehicles Research Articles

Stable nullspace adaptive parameter identification of 6 degree-of-freedom plant and actuator models for underactuated vehicles: Theory and experimental evaluation

Model-based approaches to navigation, control, and fault detection that utilize precise nonlinear models of vehicle plant dynamics will enable more accurate control and navigation, assured autonomy, and more complex missions for such vehicles. This paper reports novel theoretical and experimental results addressing the problem of parameter estimation of plant and actuator models for underactuated underwater vehicles operating in 6 degrees-of-freedom (DOF) whose dynamics are modeled by finite-dimensional Newton-Euler equations. This paper reports the first theoretical approach and experimental validation to identify simultaneously plant-model parameters (parameters such as mass, added mass, hydrodynamic drag, and buoyancy) and control-actuator parameters (control-surface models and thruster models) in 6-DOF. Most previously reported studies on parameter identification assume that the control-actuator parameters are known a priori. Moreover, this paper reports the first proof of convergence of the parameter estimates to the true set of parameters for this class of vehicles under a persistence of excitation condition. The reported adaptive identification (AID) algorithm does not require instrumentation of 6-DOF vehicle acceleration, which is required by conventional approaches to parameter estimation such as least squares. Additionally, the reported AID algorithm is applicable under any arbitrary open-loop or closed-loop control law. We report simulation and experimental results for identifying the plant-model and control-actuator parameters for an L3 OceanServer Iver3 autonomous underwater vehicle. We believe this general approach to AID could be extended to apply to other classes of machines and other classes of marine, land, aerial, and space vehicles.

A note on the predictive control of non‐holonomic systems and underactuated vehicles in the presence of drift

AbstractMotion planning and control of non‐holonomic systems is challenging. Only very recently, it has become clear how model predictive controllers for such systems can be generally furnished in the driftless case, where the key is to design a cost function conforming to the geometry arising from the non‐holonomic constraints. However, in some applications, one cannot neglect drift since the time needed to accelerate is non‐negligible, for example, when operating vehicles with high inertia or at high velocities. Therefore, this contribution extends our previous work on the class of driftless non‐holonomic systems to systems with simple kinds of actuator dynamics that allow to represent the boundedness of acceleration in the model. Moreover, we show in a prototypical example of a simple boat‐like vehicle model that a similar procedure can also work for systems that are not non‐holonomic but still under‐actuated. While the contribution is rather technical in nature, to the knowledge of the authors, it is the first time that MPC controllers with theoretical guarantees are proposed for these kinds of models. Moreover, we expect that the resulting controllers are directly of practical value since even the simpler driftless models are employed successfully in various approaches to motion planning.

A Deep Reinforcement Learning-Based Path-Following Control Scheme for an Uncertain Under-Actuated Autonomous Marine Vehicle

In this article, a deep reinforcement learning-based path-following control scheme is established for an under-actuated autonomous marine vehicle (AMV) in the presence of model uncertainties and unknown marine environment disturbances is presented. By virtue of light-of-sight guidance, a surge-heading joint guidance method is developed within the kinematic level, thereby enabling the AMV to follow the desired path accurately. Within the dynamic level, model uncertainties and time-varying environment disturbances are taken into account, and the reinforcement learning control method using the twin-delay deep deterministic policy gradient (TD3) is developed for the under-actuated vehicle, where path-following actions are generated via the state space and hybrid rewards. Additionally, actor-critic networks are developed using the long-short time memory (LSTM) network, and the vehicle can successfully make a decision by the aid of historical states, thus enhancing the convergence rate of dynamic controllers. Simulation results and comprehensive comparisons on a prototype AMV demonstrate the remarkable effectiveness and superiority of the proposed LSTM-TD3-based path-following control scheme.

Range observer‐based formation control for heterogeneous spatial underactuated vehicle networks

AbstractIn this work, we solve the distributed formation control problem for heterogeneous spatial underactuated vehicle networks subject to switching topologies. We consider the spatial rigid body model of underwater and aerial vehicles with one translational actuator for propulsion and three rotational actuators, without any simplification. A distributed finite‐time sliding mode observer is designed to estimate the ranges between vehicles based on the bearing angles, and thus, the control design does not require relative position or distance measurements. A coordinate transformation is proposed to define continuous reference velocity trajectories under switching topologies. Then, based on the cascade structure, a distributed formation protocol is presented which guarantees the global asymptotic convergence for the closed‐loop system. The formation controller has a simple structure, requires only neighbor‐to‐neighbor information exchange, and all the measurements may be obtained using simple onboard sensors. Numerical simulations for a group of heterogeneous spatial underactuated vehicles including autonomous underwater vehicles and quadrotors are presented.

A Survey on Model-Based Control and Guidance Principles for Autonomous Marine Vehicles

With the increasing number of applications for both surface and underwater autonomous vehicles, a great amount of control methods and guidance principles has been developed over the years. This work proposes a review of the most common of these methods. It is mainly focused on model-based nonlinear control methods and guidance principles. Notably, this work details examples and variations of model-based linearizing controllers, applications of line of sight guidance, sliding mode controllers and several other less common control methods for both fully-actuated and underactuated vehicles. Additionally, this work proposes an alternative definition of underactuation with respect to the task allowing for a better understanding of the consequences of underactuation on control. Comparison of fully-actuated and underactuated cases shows how control laws can be used to solve the problems of underactuation and what mechanisms can be used to compensate for the lack of actuation on a degree of freedom. The reviewed methods are compared and discussed with respect to their capabilities, limitations and suitability for typical tasks.

Optimal robust path tracking control for multi-constrained underactuated vehicles based on uncertainty orthogonal decomposition

In this article, an optimal robust constraint-following control is proposed for the underactuated vehicle path tracking problem. First, an underactuated dynamic model is established according to Udwadia–Kalaba (UK) equation, and the system uncertainty is decomposed into matching and mismatching portions based on the system geometric characteristics. The mismatching uncertainty is orthogonal to task space; thus, its influence on system stability is eliminated. Second, the diffeomorphism method is used to creatively set inequality and equality constraints into new equality constraints, and a robust control method for front steering vehicles with parameter-tunable is proposed. Third, an optimal design scheme is proposed for the tunable parameters to minimize the comprehensive index of system performance and control cost. Carsim-Simulink co-simulation shows the effectiveness of the proposed optimal robust control. This article creatively solves the problem of optimal robust control for path tracking of multi-constrained underactuated vehicles.

A Novel 3D Path Following Scheme for a Class of Underactuated Underwater Vehicles with Unconventional Actuation

A 3D path following algorithm involving a novel motion control methodology is investigated for use on a new class of autonomous underwater vehicle (AUV). Unlike standard path following AUV control algorithms for underactuated vehicles, where roll perturbations are avoided, this unconventional algorithm utilizes active roll control to achieve a desired heading. The desired heading is calculated using traditional look-ahead techniques, and is achieved by performing a roll rotation to align the body-fixed yaw plane with the desired heading, and then a yaw rotation is performed to achieve that desired heading. It is demonstrated that this new path following algorithm achieves good tracking results, but experiences complications for increased forward velocities. It is also demonstrated that the complications at higher velocities can be overcome with adaptive adjustment of the look-ahead algorithm parameters.

A fully-actuated quadcopter representation using quaternions

Recent advances in practical fields like robotics and the miniaturisation of many sensors and actuators have turned autonomous vehicles into a reality. These systems come in many shapes and forms depending on the medium and their design but can be classified in one of two categories according to their mechanical configuration and number of actuators: fully-actuated and under-actuated vehicles; the second group still poses many challenges for the automatic control and robotics communities. This work introduces an easy methodology, based on quaternions, for designing controllers for a class of under-actuated systems, such as multicopter vehicles. The methodology starts from a fully-actuated representation of the system and adapts it to be implemented in under-actuated systems. In addition, it allows the easy development of controllers without taking care the coupled dynamics of the system. The proposed approach is based on Lyapunov's stability theory and is proven for certain criteria of the system's dynamics. The quadcopter configuration is used to validate the proposed methodology in simulations and in experimental tests. Abbreviations: AGV: autonomous ground vehicle; AUV: autonomous underwatervehicle; DoF: degree(s) of freedom; ESC: energy shaping controller; SFC: statefeedback controller; SSC: separated saturations controller; UAV: unmanned aerialvehicle

Path Tracking Control for Underactuated Vehicles With Matched-Mismatched Uncertainties: An Uncertainty Decomposition Based Constraint-Following Approach

This paper presents a robust path tracking control method by utilizing the ideology of constraint-following approach for uncertain underactuated autonomous vehicles. The uncertainties are bounded with an unknown boundary. They do not all fall within the range space of the input matrix. Based on kinematic relations between the desired path and vehicle, the path tracking task is transformed into an equality constraint of the vehicle lateral dynamics states. The control goal is to make the underactuated vehicle follow the constraint, thus realizing the desired tracking performance. The constraint-following robust control (CFRC) is designed in two steps. First, a servo control design for the nominal system is devised without considering uncertainty and initial constraint deviation. Second, the uncertainty is meticulously decomposed into matched and mismatched portions based on the geometric structural characteristics of the constraint dynamics system. As a result, since the mismatched uncertainty is orthogonal to the constraint-following geometric space, it “disappears” in the stability analysis. The matched uncertainty is estimated by a self-adjusting leakage type adaptive law. On this basis, a robust control is designed based on the estimated matched uncertainty. Through Lyapunov minimax analysis, the proposed control method guarantees the approximate constraint-following performance. Finally, the TruckSim–Simulink co-simulations and real vehicle experiments are presented. The results show that the proposed control can robustly realize excellent tracking performance in the presence of time-vary uncertainties.

Fast Finite-Time Path-Following Control of Unmanned Surface Vehicles with Sideslip Compensation and Time-Varying Disturbances

This paper studies the fast finite-time path following of underactuated unmanned surface vehicles (USV) with sideslip compensation, time-varying disturbances and input saturation. In the guidance module, the fast finite-time predictor-based line-of-sight (FFTPLOS) is proposed to overcome the large guidance angle and high-frequency oscillation and eliminate the sideslip angle with finite time. Then, the robust finite-time feedback control is applied to keep the vehicle following the desired path in the control module, where the reduced-order extended state observers (ROESO) are applied to deal with time-varying disturbances. Additionally, fast finite-time auxiliary dynamic systems with smoothly switching functions (FFTADS-SSF) achieve the saturation constraints on actuators with low consumption. The stability analysis proves that the guidance-control system of USVs is uniformly ultimately bounded stable within finite time. The effectiveness and performance of this proposed scheme are superior to the comparison schemes.

Simplified Trajectory-Tracking Method for an Under-Actuated USV

Traditional control methods designed for the trajectory tracking problem of under-actuated vehicles often aim to directly stabilize the tracking-error system of differential equations to the origin. This often results in complex control algorithms. This paper introduces a simplified control method for the trajectory tracking problem of an under-actuated Unmanned Surface Vehicle (USV). The proposed method consists of a guidance law for intermediate variables, which are the pseudo-yaw angle and the pseudo-surge velocity, and a Proportional-Integral (PI) controller. The control term for surge velocity is designed to be bounded, which reduces undesired instability. A model is built based on linear dynamics equations and parameters of an USV. The proposed tracking method is applied to the model to track different trajectories in simulations. The simulation results show that the proposed method effectively tracks different trajectories under various initial conditions. The control term for surge velocity remains stable despite the relatively large initial tracking-error condition.

Path following of underactuated vehicles via integral line of sight guidance and fixed‐time heading control

Path following of underactuated vehicles via integral line of sight guidance and fixed‐time heading control

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle's model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller.

Time-Varying Formation Control for Heterogeneous Planar Underactuated Multivehicle Systems

Abstract This paper presents a distributed control approach for time-varying formation of heterogeneous planar underactuated vehicle networks without global position measurements. All vehicles in the network are modeled as generic three degree-of-freedom planar rigid bodies with two control inputs, and are allowed to have nonidentical dynamics. Feasible trajectories are generated for each vehicle using the nonholonomic constraints of the vehicle dynamics. By exploiting the cascaded structure of the planar vehicle model, a transformation is introduced to define the reduced order error dynamics, and then, a sliding-mode control law is proposed. Low-level controller for each vehicle is derived such that it only requires relative position and local motion information of its neighbors in a given directed communication network. The proposed formation control law guarantees the uniform global asymptotic stability (UGAS) of the closed-loop system subject to bounded uncertainties and disturbances. The proposed approach can be applied to underactuated vehicle networks consisting of mobile robots, surface vessels, and planar aircraft. Simulations are presented to demonstrate the effectiveness of the proposed control scheme.

Safe trajectory tracking for underactuated vehicles with partially unknown dynamics

<p style='text-indent:20px;'>Underactuated vehicles have gained much attention in the recent years due to the increasing amount of aerial and underwater vehicles as well as nanosatellites. The safe tracking control of these vehicles is a substantial aspect for an increasing range of application domains. However, external disturbances and parts of the internal dynamics are often unknown or very time-consuming to model. To overcome this issue, we present a safe tracking control law for underactuated rigid-body dynamics using a learning-based oracle for the prediction of the unknown dynamics. The presented approach guarantees a bounded tracking error with high probability where the bound is explicitly given. With additional assumptions, asymptotic stability of the tracking error is achieved. A numerical example highlights the effectiveness of the proposed learning-based control law.</p>

Online Learning-Based Trajectory Tracking for Underactuated Vehicles With Uncertain Dynamics

Underactuated vehicles have gained much attention in the recent years due to the increasing amount of aerial and underwater vehicles as well as nanosatellites. Trajectory tracking control of these vehicles is a substantial aspect for an increasing range of application domains. However, external disturbances and parts of the internal dynamics are often unknown or very time-consuming to model. To overcome this issue, we present a tracking control law for underactuated rigid-body dynamics using an online learning-based oracle for the prediction of the unknown dynamics. We show that Gaussian process models are of particular interest for the role of the oracle. The presented approach guarantees a bounded tracking error with high probability where the bound is explicitly given. A numerical example highlights the effectiveness of the proposed control law.

Formation Control for Heterogeneous Spatial Underactuated Vehicles Using Bearing Measurements

In this work, we solve the distributed formation control problem for heterogeneous spatial underactuated vehicles subject to switching topologies. We consider the spatial rigid body model of vehicles with one translational actuator for propulsion and three rotational actuators. A finite-time sliding mode observer is designed to estimate the ranges between vehicles based on the bearing measurements. A generalized Slotine-Li transformation is proposed to define continuous reference velocity trajectories under switching topologies. Based on the cascade structure, a distributed formation protocol is presented which guarantees the global asymptotic convergence for the closed-loop system. Numerical simulations on a group of spatial underactuated vehicles including quadcopters and underwater vehicles are presented.

Asymptotic stabilization of underactuated surface vehicles with actuator saturation.

This paper investigates the problem of global asymptotic stabilization of underactuated surface vessels (USVs) with input saturation. A novel input transformation is presented, so that the USV system can be transformed to a cascade structure. For the obtained system, the improved fractional power control laws are proposed to ensure input signals do not exceed actuator constraints and enhance convergence rates. Finally, stabilization and parameter optimization algorithm of USVs are proposed. Simulations are given to demonstrate the effectiveness of the presented method.

Concise leader-follower formation control of underactuated unmanned surface vehicle with output error constraints

In this paper, a concise leader-follower formation control approach is presented for a group of underactuated unmanned surface vehicle with dynamic system uncertainties and external environment disturbances, where the output errors are required to be within constraints. To settle the output error constraints, a standard barrier Lyapunov function (BLF) is incorporated into the backstepping control method. Furthermore, the “differential explosion” problem of virtual control laws is avoided by introducing the dynamic surface control. To estimate the unknown dynamic terms, an adaptive neural network is designed and a nonlinear disturbance observer is adopted to compensate for the approximation errors of neural network and ocean environment disturbances. Under the constraint of output error, the presented controller based on standard BLF has simpler structure and better control performance than depended on tan-type BLF. The presented controller can ensure that the formation errors converge to a small range around zero, while the output error constraint requirements are met. All signals in the closed-loop system are bounded, and the numerical simulation further shows the effectiveness of the presented control scheme.

Leader–follower formation stabilization and tracking control for heterogeneous planar underactuated vehicle networks

In this paper, we solve the distributed leader–follower simultaneous formation stabilization and tracking control problem for heterogeneous planar underactuated vehicle networks without global position measurements of the followers. The vehicles in the network are modeled as generic 3-DOF planar rigid bodies with two control inputs, and are allowed to have identical or non-identical dynamics. By incorporating graph theory, passivity-based control, partial stability theory, Matrosov’s theorem and the persistence of excitation concept, a smooth formation control scheme is proposed to simultaneously address the formation stabilization and formation tracking problems without switching. Moreover, the structure of the controller is relatively simple compared to the existing controllers in the literature, and thus, is practical and easy to implement. Simulations on a group of underactuated vehicles including nonholonomic mobile robots and surface vessels are presented to demonstrate the effectiveness of the proposed control scheme.