Unknown Inertia Parameters Research Articles

Fault‐tolerant adaptive tracking control for spacecraft attitude with asymptotic convergence

AbstractIn this paper, we present a novel spacecraft attitude adaptive tracking control strategy that addresses the challenges posed by unknown inertia parameters, bounded unstructured uncertainties, and various actuator faults. To mitigate the adverse effects of these multiple uncertainties, our proposed control algorithm utilizes a simple tracking‐error feedback and compensation term, which only requires two adaptive parameters. This approach ensures asymptotic tracking convergence by employing an infinitely integrable inequality that incorporates saturation functions. As a result, the complexity of controller design and computational burden are significantly reduced. Finally, several numerical simulations are conducted to validate the feasibility and superiority of our proposed controller.

A Model-Free Online Learning Control for Attitude Tracking of Quadrotors

This paper investigates the problem of attitude tracking in quadrotor unmanned aerial vehicles (UAVs) using a model-free online learning control (MFOLC) scheme. The attitude system, which is represented by unit quaternions, is considered in the presence of uncertain and unknown inertia parameters, time-varying external disturbances, and angular velocity measurement noise. A computationally low-cost control scheme consisting of a model-free baseline controller and a module capable of learning from previous control input is designed. The proposed controller does not require precise inertial parameters and does not involve feedforward terms that use these parameters and true system states. This ensures that the approach can protect the control effort from sensor noise as well as parameter uncertainty. We also show that all the signals in the closed-loop system are uniformly ultimately bounded. Comparative simulations and real-world experiments are conducted for validation, which demonstrate the effectiveness and fine performance of the proposed scheme.

Distributed GNE Seeking Strategy for Second-Integrator Multiplayer Systems Over Directed Topologies.

This article studies the generalized Nash equilibrium (GNE) seeking problem of second-integrator multiplayer systems. In particular, each player is endowed with an individual payoff function with respect to collective decision variables, and simultaneously, a coupling inequality constraint and a set constraint are imposed to each player. The players communicate with their local neighbors over a directed topology. To begin with, a distributed-observer-based seeking strategy is synthesized by leveraging a proper composite variable. It is first demonstrated using nonsmooth analysis that the established distributed observer enables each player to accurately estimate the decision variables of others in terms of a strongly connected topology condition. Upon this basis, all the decision variables are then shown to converge to the expected GNE asymptotically borrowing from convex theory. In addition, three extension results are also given under the built GNE seeking framework. First, under the postulation that the velocity information is unavailable, a velocity-free distributed GNE seeking strategy is synthesized for second-integrator systems by implementing a proper auxiliary dynamics. Second, we consider nonlinear Euler-Lagrange systems with unknown inertia parameters and synthesize an improved distributed GNE seeking strategy resorting to an adaptation technique. Third, we focus on integrator chain systems and synthesize a modified distributed GNE seeking strategy using a new composite variable based on a proper coordinate transformation. For three extension cases, we all show in detail the achievement of the GNE seeking objective. Finally, a practical example is simulated to confirm the built GNE seeking results.

Attitude Tracking Adaptive Control of a Geocentric Polar Displaced Solar Sail

To deal with the attitude tracking control problem of a struck or pierced geocentric polar displaced solar sail (GPDSS), an attitude adaptive control strategy is proposed in this paper under the complex conditions of unknown inertial parameters, external disturbance and input saturation. First, on the basis of a flexible solar sail spacecraft attitude dynamics model with damping terms and vibration initial values, an integrated disturbance term, including inertial parameter uncertainties and external disturbance, is constructed. Second, a radial basis function neural network is applied to design a disturbance estimator with an adaptive law to estimate the integrated disturbance in real time. Then, a sliding-mode controller with fixed-time convergence in the reach phase and finite-time stability in the sliding phase is designed, and stability analysis is conducted by using the Lyapunov theory. Finally, comparative simulations with a linear sliding-mode controller and numerical simulations under various workings are performed. The results show that the designed adaptive control strategy can effectively achieve the attitude tracking control of the GPDSS.

Adaptive Tracking of Large-Angle Maneuvers for Spacecraft Equipped with an Active Pointing Ultraquiet Platform

An adaptive controller for the tracking of large-angle maneuvers is proposed for spacecraft equipped with an active pointing ultraquiet platform (AQP). The inertial parameters of the spacecraft and the payload (supported by the AQP) are estimated online, whereas the parameters of the AQP are assumed to be precisely known. To enable the derivation of the proposed controller, a novel dynamic model of AQP spacecraft was derived, which employs relative motion variables for the payload and is linear in the unknown inertial parameters. A Lyapunov-like argument was used to prove the local asymptotical stability of the closed-loop system, and the original controller was simplified further to a physically more intuitive proportional-differential (PD) plus adaptive feed-forward controller. The superior tracking performance of the proposed controller compared with that of a standard PD plus nonadaptive feed-forward controller was shown via numerical simulation. It also was shown that the estimates of a selected set of unknown inertial parameters will converge to their true values if a certain kind of maneuver trajectory is tracked.

Adaptive fault‐tolerant control for a class of flexible air‐breathing hypersonic vehicles

AbstractIn this paper, a novel adaptive fault‐tolerant control (FTC) scheme is proposed for a class of flexible air‐breathing hypersonic vehicles with unknown inertial and aerodynamic parameters and even input constraints. The fault model under consideration covers the case that all actuators suffer from unknown time‐varying faults. In the controller design and stability analysis, we introduce new Lyapunov functions, some differentiable auxiliary functions, a bound estimation approach, and a Nussbaum function, which help us successfully circumvent the obstacle caused by the faults, input constraints, and flexible modes. In addition to higher reliability, the proposed scheme is able to ensure that all closed‐loop signals are globally uniformly bounded and to steer the tracking errors of altitude and velocity into predefined arbitrarily small residual sets. As a result, the tracking accuracy can be designated in advance. Simulation results illustrate the effectiveness of the proposed scheme.

Projection Scheme and Adaptive Control for Symmetric Matrices With Eigenvalue Bounds

A projection scheme to handle eigenvalue bounds for adaptive control with uncertain symmetric matrix parameters is introduced. Conventional parameter projection techniques are generally unable to handle explicit eigenvalue bounds. The continuous projection scheme presented here maintains the closed-loop stability properties for adaptive controllers while simultaneously satisfying <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> available eigenvalue bounds of the uncertain symmetric matrix valued parameters. The projection scheme uses the eigen decomposition of the symmetric matrix parameter to project its eigenvalues to lie within the prescribed bounds. The eigenvalues of the symmetric matrix may be lower bounded or upper bounded or both. A direct adaptation over the eigenvalues and the eigen projections of the symmetric matrix parameter is also derived to help circumvent expensive eigen decomposition calculations. The new projection here shows improved performance in numerical simulations of rigid body attitude tracking control and trajectory tracking of robotic manipulators with unknown inertia parameters.

Adaptive finite-time control for six-degree-of-freedom leader-following spacecraft formation using twistors

An adaptive finite-time attitude and position coupled tracking controller for six-degree-of-freedom (6-DOF) leader-following spacecraft formation is proposed in this paper. The relative motion of the follower with respect to its desired pose is represented by twistors in a unified way without state redundancy. A fast terminal sliding surface is proposed for the twistor-based dynamic system to achieve finite-time convergence. Then an adaptive finite-time controller is developed with the unknown inertial parameters of the follower spacecraft and the upper bounds of the disturbances estimated by elaborately designed adaptive laws. The finite-time convergence of the closed-loop system is proven via Lyapunov analysis. In addition, an simple but effective strategy is proposed to eliminate the attitude unwinding phenomenon. The proposed adaptive finite-time control scheme possesses faster convergence, higher control accuracy, and more preferable control inputs. In addition, the possible numerical difficulties caused by logarithmic function of dual quaternions is avoided. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.

Optimal detumbling strategy for a non-cooperative target with unknown inertial parameters using a space manipulator

Capturing tumbling target is considered as one of the greatest challenges in on-orbit service missions due to tumbling motion and parameter uncertainty of the space non-cooperative target. The tumbling motion of the target should be attenuated as quickly as possible before grasping to avoid the unexpected collisions and possible damages to the space manipulator or the target, which means the shortest-time detumbling trajectory is necessary. In many studies about the optimal detumbling trajectory planning the inertial parameters of the target have been assumed to be accurately known, which is usually difficult for a non-cooperative target so that parameter identification is needed before planning a optimal detumbling trajectory. In this paper, a novel strategy for parameter identification and detumbling of a tumbling target by a space manipulator is proposed. The strategy includes two phases. First, unknown inertial parameters of the target are identified in finite-time by a new estimation method with the assumption of interval excitation (IE), which relaxes the strict persistent excitation (PE) condition required in most prior studies. Second, the shortest-time detumbling trajectory of the tumbling target is generated by formulating a time-optimal control problem (OCP) in which the target attitude bounds and the limitations of the contact force as well as the relative velocity between the space manipulator and the target are represented as extended dynamical sub-systems and saturation functions. Then, the Calculus of Variations method is used to solve the OCP to obtain a high accuracy solution. During two phases, the contact force between the space manipulator and the target is utilized to generate external moment for identifying the inertia parameters of the target and detumbling the target. Meanwhile, a unified hybrid impedance control framework is applied to the space robot to track the desired contact force and motion trajectory. The whole strategy is verified by a space manipulator capturing a tumbling target, and numerical simulations demonstrate the effectiveness of the proposed methods.

Rotation matrix-based finite-time attitude synchronization control for flexible spacecrafts with unknown inertial parameters and actuator faults

This paper studies the distributed attitude synchronization control for flexible spacecrafts with the consideration of unmeasurable modal variable and partial loss of actuator effectiveness faults. The designed rotation matrix-based controller consisted of the basic pattern and the supplementary pattern. Based on a connected undirected graph, the original graph was established on the assumption of inexistent actuator fault, and the unavailable flexible dynamics was approximately described by neural networks (NNs). By using the minimum learning parameter (MLP) algorithm, the finite-time stability of the formation system was improved and the burdensome computation was lightened. A modified sliding mode surface (SMC) is presented which can avoid singularity and the tracking errors can be stabilized to the equilibrium within finite time.

Robust adaptive tracking control for uncertain nonholonomic mobile manipulator

In the research put forth, a robust adaptive control method for a nonholonomic mobile manipulator robot, with unknown inertia parameters and disturbances, was proposed. First, the description of the robot’s dynamics model was developed. Thereafter, a novel adaptive sliding mode control was designed, to which all parameters describing involved uncertainties and disturbances were estimated by the adaptive update technique. The proposed control ensures a relatively good system tracking, with all errors converging to zero. Unlike conventional sliding mode controls, the suggested is able to achieve superb performance, without resulting in any chattering problems, along with an extremely fast system trajectories convergence time to equilibrium. The aforementioned characteristics were attainable upon using an innovative reaching law based on potential functions. Furthermore, the Lyapunov approach was used to design the control law and to conduct a global stability analysis. Finally, experimental results and comparative study collected via a 05-DoF mobile manipulator robot, to track a given trajectory, showing the superior efficiency of the proposed control law.

Dynamic scaling‐based adaptive control without scaling factor: With application to Euler–Lagrange systems

AbstractA modular dynamic scaling‐based immersion and invariance (I&amp;I) adaptive control framework for a class of nonlinear system with parametric uncertainties is presented in this paper. The framework is based on an invariant manifold approach which allows for predefined target dynamics to be assigned to the closed‐loop systems. The integrability obstacle typically inherent to I&amp;I methodology is overcome by the matrix reconstruction and dynamic scaling technique. The prominent feature is that this methodology can be implemented without scaling factor, and hence the introduction of the scaling factor is just to prove the additive disturbance brought by the matrix reconstruction can be eliminated by constant feedback gains. Moreover, the bounded robustness against three different types of disturbance is verified. As an application, Euler‐Lagrange systems with unknown inertia parameters are applied to illustrate the effectiveness of the proposed method.

Distributed Continuous-Time Algorithm for Constrained Optimization of Networked Euler–Lagrange Systems

This article studies a distributed constrained optimization problem of multiple agents characterized by Euler-Lagrange systems with unknown inertial parameters. The optimization objective is to compute a feasible solution within the intersection of a series of constrained sets such that a global payoff function summed by a group of local ones is minimized. Meanwhile, each local payoff function and constrained set are just privately available to their respective agent. To accomplish the concerned constrained optimization objective, a fully distributed continuous-time algorithm resorting to a projection-based auxiliary dynamics is synthesized without using global topology information. The proposed distributed optimization algorithm is privacy-preserving in the sense that no actual state information is exchanged between distinct agents during the seeking progress. Besides, the associated stability analysis is carried out in terms of the Lyapunov theorem. Finally, a source localization example is performed to verify the effectiveness of the proposed distributed optimization algorithm.

Neural Network-Based Finite-Time Fault-Tolerant Control for Spacecraft without Unwinding

In this paper, we focus on solving the problems of inertia-free attitude tracking control for spacecraft subject to external disturbance, unknown inertial parameters, and actuator faults. The robust control architecture is designed by using the rotation matrix and neural networks. In the presence of external disturbance and parametric uncertainties, a fault-tolerant control (FTC) scheme synthesized with the minimum-learning-parameter (MLP) algorithm is proposed to improve the reliability of the system when unknown actuator faults occur. These methods are developed based on backstepping to ensure that finite-time convergence is achievable for the entire closed-loop system states with low computational complexity. The validity and advantage of the designed controllers are highlighted by using Lyapunov-based analysis. Finally, the simulation results demonstrate the satisfactory performance of the developed controllers.

Adaptive Closed-Loop Identification and Tracking Control of an Aerial Vehicle with Unknown Inertia Parameters

Abstract In this paper, the problem of adaptive closed-loop parameter estimation and tracking control of a six degree of freedom (6-DOF) nonlinear quadrotor unmanned aerial vehicle (UAV) is studied. To manage the complexity of the problem, the system dynamics is decomposed into two subsystems, i.e. translational dynamics and rotational dynamics. A nested control architecture is adopted to develop both adaptive tracking control and parameter estimation. To stabilize the outer loop, a virtual control input is proposed using a proportional-derivative (PD) controller to track the x, y and z positions. The rotational dynamics of UAV contains unknown inertia parameters appearing in the control structure as well as in a nonlinear dynamic term. An adaptive tracking scheme is designed using the certainty equivalence principle to handle both parameter estimation and tracking control in a closed-loop. The idea behind the controller design is to cancel the nonlinear term in the inner loop by estimating the unknown system parameters. The stability of the whole closed-loop system is proved with a rigorous analytical study. Moreover, the performance of the proposed controller is verified with several numerical analyses.

Minimum-learning-parameter-based anti-unwinding attitude tracking control for spacecraft with unknown inertia parameters

This paper investigates the finite-time attitude tracking control problem for rigid spacecraft exposed to the external disturbance and unknown inertial parameters. Initially, the basic controller is developed under the assumption that the inertial parameters and the upper bound of external disturbances are available to the designer. However, this assumption is inapplicable in practical applications. Considering this limitation, adaptive laws and Minimum-learning- parameter (MLP) algorithm are employed in the second controller to estimate the unknown system dynamics. Finite-time stability for tracking errors is achievable under the proposed methods. Though theoretical analysis and numerical simulations, effectiveness of the proposed controllers has been validated.

Robust coordination control of a space manipulator to detumble a non-cooperative target

This paper presents a robust detumbling strategy for a spacecraft equipped with a robotic manipulator to detumble a non-cooperative target with unknown inertial parameters. Reported detumbling strategies in the literature have been formulated with the assumption of accurately known target inertial parameters (mass, inertia tensor, center of mass location) and without consideration of magnitude limits on the robotic spacecraft’s control inputs. In reality, it is unrealistic to assume accurate knowledge of the target’s inertial parameters and the robotic spacecraft will be subjected to limits on its control inputs. In this paper, a novel detumbling strategy is presented to detumble targets with unknown parameters utilizing only bounds on their inertial parameters. A desired detumbling trajectory is delineated using only bounds on the target’s inertial parameters and subjected to end-effector force/torque limits. Magnitude constraints on the robotic spacecraft are taken into account by modeling them with a hyperbolic tangent function, which results in a system that is non-affine in its control inputs. To facilitate the development of the detumbling controller, an augmented model of the robotic spacecraft is formulated. Using bounds on the target’s inertial parameters, robust adaptive control approach is utilized to design the detumbling controller with the backstepping technique to ensure successful detumbling of the unknown target attached to the end-effector and rejection of its momentum. Numerical simulations have demonstrated the effectiveness of the proposed method.

Inertial parameter estimation and control of non-cooperative target with unilateral contact constraint

In this paper, the relative sliding motion between the target and the manipulator’s end-effector is considered and characterized as a unilateral contact constraint. A new possible solution is presented to estimate the inertial parameters of a non-cooperative target while the relative sliding motion exists. First, the detailed analysis of the dynamical model is presented, and a parameter-explicit linear time-varying model is obtained. Then, an extended state observer is constructed based on the new model, which can effectively estimate the unknown inertial parameters of the target when relative sliding motion exists. As the modified reactionless controller requires the knowledge of inertial parameters, a hybrid post-capture control scheme is also established based on the switch law between different controllers. The correctness and efficiency of the proposed algorithm are validated by numerical simulation, which proves a potential framework for the non-cooperative target post-capture operation.

High‐performance PMSM self‐tuning speed control system with a low‐order adaptive instantaneous speed estimator using a low‐cost incremental encoder

AbstractIn practical industrial applications, the control performance in a wide speed range is hard to ensure, especially under the low‐speed condition with a low‐cost incremental encoder, while the unknown structure parameters may also degrade the tracking performance. This paper proposes a low‐order adaptive instantaneous speed estimator (AISE) and a self‐tuning control strategy to promote the speed control performance in a wide speed range with unknown inertia parameters. Together with the adaptive‐Kalman‐filter‐based AISE, a novel measurement noise variance updating scheme, which allows more appropriate compensation in the different speed range than fixed error variance, is introduced through the theoretical analysis based on probability and stochastic process. Moreover, an easy‐to‐implement self‐tuning law, integrated with an online recursive‐least‐square‐based parameters identification method, is developed to tune the speed controller, while the AISE is also adjusted online to ensure the control performance with a considerable variation of load inertia. All strategies were implemented in a TMS320F28335‐based permanent magnet synchronous motor (PMSM) control system with a low‐cost 2500‐line incremental encoder, and the results demonstrated the effectiveness of the proposed techniques.

Finite‐time adaptive fault‐tolerant control for rigid spacecraft attitude tracking

AbstractThis paper provides a new solution for the finite‐time attitude maneuvers of rigid spacecraft. Uncertainties involving unknown inertial parameters, external disturbances and actuator failures are taken into account. With an effort to achieve attitude tracking despite the impact of uncertainties, a non‐singular terminal sliding mode (NTSM) manifold consisting of attitude errors and angular velocity errors is first constructed. After that, a simple but efficient adaptive updating law is derived to estimate the upper bound of the lumped unknown function in the derivative of sliding surface. Combining NTSM technology and pure adaptive control, a chattering‐free fault‐tolerant controller is presented. The premise assumptions on uncertainties in most of the existing achievements are eliminated, which makes the controller less constrained and more practical. The rigorous proof of finite‐time stability is provided and the convergent regions of tracking errors are explicitly expressed. Finally, numerical simulation is conducted to verify the effectiveness of the proposed control scheme and the comparison experiments with relevant literature demonstrate the satisfactory performances.