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The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller (ENMPC) by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization (QPIO).

The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory. Since the ENMPC has high demand for the state equation, the trajectory needed to be differentiated many times. When the trajectory is complicate or discontinuous, QPIO is proposed to linearize the trajectory. Then the linearized trajectory will be used in the ENMPC.

Applying the QPIO algorithm allows the unequal distance sample points to be acquired to linearize the trajectory. Comparing with the equidistant linear interpolation, the linear interpolation error will be smaller.

Small-sized quadrotors were adopted in this research to simplify the model. The model is supposed to be accurate and differentiable to meet the requirements of ENMPC.

Traditionally, the quadrotor model was usually linearized in the research. In this paper, the quadrotor model was kept nonlinear and the trajectory will be linearized instead. Unequal distance sample points were utilized to linearize the trajectory. In this way, the authors can get a smaller interpolation error. This method can also be applied to discrete systems to construct the interpolation for trajectory tracking.

The purpose of this paper is to analyze the results of the Jacobian matrix linearization of the satellite attitude dynamics with modified Rodriguez parameters (MRP) as attitude representation.

The satellite dynamics is linearized using Jacobian differentiation around origin and reference values of the MRP. The controller is designed through linear quadratic regulation approach.

It is found that, for both cases the overall system converges but there exists a tracking error. The error can be reduced by increasing the controller coefficients in both cases however cannot be eliminated. In the case of linearization around zero, the torque requirements are quite higher than the case of linearization around the reference attitude trajectory.

The attempt of Jacobian linearization of a satellite dynamics with the MRP as the attitude representation constitutes the value of this paper. In addition, the results obtained in the derivations may be used in future research.

The purpose of this paper is to show the feasibility of constrained model predictive control (MPC) for sophisticated helicopter models which are derived by physical considerations.

Physics‐based modeling is used to create control‐oriented helicopter models. Advanced constrained controllers are designed and tested for these sophisticated models.

The helicopter models are valid and constrained MPC shows considerable promise for robust tracking.

MPCs can be implemented for highly constrained helicopter flights.

A complete process of control‐oriented, physics‐based model development for helicopters followed by MPC design is developed. It is also proved that constrained MPC can be used and implemented online to robustly track discontinuous helicopter trajectories with heterogeneous constraints, even when the models are sophisticated and physics based.

The purpose of this paper is to design a robust angle-of-attack (AOA) tracking control system for the hypersonic reentry vehicle (HRV) based on the linear parameter varying (LPV) theory, as the aerodynamic coefficients of the hypersonic vehicle vary quickly during the reentry phase.

First, longitudinal moment trim is done along the desired flight trajectory. The linearized system at each trim point is built and the dynamic characteristics analysis is made. Then the LPV control law with parameter-dependent quadratic Lyapunov function (PDQLF-LPV) is applied to design the AOA tracking autopilot at each trim point. Frequency performance of the autopilot is assessed and the step response simulation is conducted to validate the effectiveness of the control system. Finally, actual AOA command tracking simulations based on the time-varying nonlinear model are carried out to test the correctness and robustness of the PDQLF-LPV autopilot.

Analysis results demonstrate that the PDQLF-LPV control system can track the AOA command perfectly during the whole flight envelop with dynamics parameter variation or disturbances, which indicates that it is effective to integrate the PDQLF-LPV control theory with a parameter-varying reference model for control system design of HRV.

A reference model with varying parameters is utilized to guarantee the transient performance of the autopilot, and induced L2-norm analysis is introduced to describe and guarantee the robust stability of the autopilot.

Many important electronic systems are modelled by discrete‐time equations with nonlinearities that are discontinuous and piecewise‐linear, often arising as a result of quantization. Approximations based on linearization – the standard engineering response to nonlinearity – are often quite unhelpful in these systems, because of the form of the nonlinearity. Certain methods and results have been developed over a number of years for the analysis of discontinuous piecewise‐linear discrete‐time dynamics. The aim of this tutorial paper is to review that body of knowledge, and to show how it can be applied to representative electronic systems.

The paper uses an important electronic circuit – the ΣΔ modulator – as a central example, and considers the dynamical behaviour exhibited by this circuit and related circuits.

The circuits under investigation exhibit complex forms of behaviour that can be explained by the application of methods of nonlinear discrete‐time dynamics.

This paper is intended to provide a brief introduction to the body of research that exists into the behaviour of nonlinear discrete‐time circuits and systems with discontinuous piecewise‐linear nonlinearities.

The purpose of this paper is to introduce a motion control method for WFF-AmphiRobot, which can effectively realize the flexible motion of the robot on land, underwater and in the transition zone between land and water.

Based on the dynamics model, the authors selected the appropriate state variables to construct the state space model of the robot and estimated the feedback state of the robot through the maximum a posteriori probability estimation. The nonlinear predictive model controller of the robot is constructed by local linearization of the model to perform closed-loop control on the overall motion of the robot. For the control problem of the terminal trajectory, using the neural rhythmic movement theory in bionics to construct a robot central pattern generator (CPG) for real-time generation of terminal trajectory.

In this paper, the motion state of WFF-AmphiRobot is estimated, and a model-based overall motion controller for the robot and an end-effector controller based on neural rhythm control are constructed. The effectiveness of the controller and motion control algorithm is verified by simulation and physical prototype motion experiments on land and underwater, and the robot can ideally complete the desired behavior.

The paper designed a controller for WFF-AmphiRobot. First, when constructing the robot state estimator in this paper, the robot dynamics model is introduced as the a priori estimation model, and the error compensation of the a priori model is performed by the method of maximum a posteriori probability estimation, which improves the accuracy of the state estimator. Second, for the underwater oscillation motion characteristics of the flipper, the Hopf oscillator is used as the basis, and the flipper fluctuation equation is modified and improved by the CPG signal is adapted to the flipper oscillation demand. The controller effectively controls the position error and heading angle error within the desired range during the movement of the WFF-AmphiRobot.

This paper aims to propose a forcefree control algorithm that is based on a dynamic model with full torque compensation is proposed to improve the compliance and flexibility of the direct teaching of cooperative robots.

Dynamic parameters identification is performed first to obtain an accurate dynamic model. The identification process is divided into two steps to reduce the complexity of trajectory simplification, and each step contains two excitation trajectories for higher identification precision. A nonlinear friction model that considers the angular displacement and angular velocity of joints is proposed as a secondary compensation for identification. A torque compensation algorithm that is based on the Hogan impedance model is proposed, and the torque obtained by an impedance equation is regarded as the command torque, which can be adjusted. The compensatory torque, including gravity torque, inertia torque, friction torque and Coriolis torque, is added to the compensation to improve the effect of forcefree control.

The model improves the total accuracy of the dynamic model by approximately 20% after compensation. Compared with the traditional method, the results prove that the forcefree control algorithm can effectively reduce the drag force approximately 50% for direct teaching and realize a flexible and smooth drag.

The entire algorithm is verified by the laboratory-developed six degrees-of-freedom cooperative robot, and it can be applied to other robots as well.

A full torque compensation is performed after parameters identification, and a more accurate forcefree control is guaranteed. This allows the cooperative robot to be dragged more smoothly without external sensors.

To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of 100:1 are often used in the joints of a robotic manipulator. This results into an actuator with large mechanical impedance (also known as nonback-drivable actuator). This in turn generates high contact forces when collision of the robotic mechanism occur and can cause humans’ injury. Another disadvantage of electric actuators is that they can exhibit overheating when constant torques have to be provided. Comparing to electric actuators, pneumatic actuators have promising properties for robotic applications, due to their low weight, simple mechanical design, low cost and good power-to-weight ratio. Electropneumatically actuated robots usually have better friction properties. Moreover, because of low mechanical impedance, pneumatic robots can provide moderate interaction forces which is important for robotic surgery and rehabilitation tasks. Pneumatic actuators are also well suited for exoskeleton robots. Actuation in exoskeletons should have a fast and accurate response. While electric motors come against high mechanical impedance and the risk of causing injuries, pneumatic actuators exhibit forces and torques which stay within moderate variation ranges. Besides, unlike direct current electric motors, pneumatic actuators have an improved weight-to-power ratio and avoid overheating problems.

The aim of this paper is to analyze a nonlinear optimal control method for electropneumatically actuated robots. A two-link robotic exoskeleton with electropneumatic actuators is considered as a case study. The associated nonlinear and multivariable state-space model is formulated and its differential flatness properties are proven. The dynamic model of the electropneumatic robot is linearized at each sampling instance with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. Within each sampling period, the time-varying linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. An H-infinity controller is designed for the linearized model of the robot aiming at solving the related optimal control problem under model uncertainties and external perturbations. An algebraic Riccati equation is solved at each time-step of the control method to obtain the stabilizing feedback gains of the H-infinity controller. Through Lyapunov stability analysis, it is proven that the robot’s control scheme satisfies the H-infinity tracking performance conditions which indicate the robustness properties of the control method. Moreover, global asymptotic stability is proven for the control loop. The method achieves fast convergence of the robot’s state variables to the associated reference trajectories, and despite strong nonlinearities in the robot’s dynamics, it keeps moderate the variations of the control inputs.

In this paper, a novel solution has been proposed for the nonlinear optimal control problem of robotic exoskeletons with electropneumatic actuators. As a case study, the dynamic model of a two-link lower-limb robotic exoskeleton with electropneumatic actuators has been considered. The dynamic model of this robotic system undergoes first approximate linearization at each iteration of the control algorithm around a temporary operating point. Within each sampling period, this linearization point is defined by the present value of the robot’s state vector and by the last sampled value of the control inputs vector. The linearization process relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. The modeling error which is due to the truncation of higher-order terms from the Taylor series is considered to be a perturbation which is asymptotically compensated by the robustness of the control algorithm. To stabilize the dynamics of the electropneumatically actuated robot and to achieve precise tracking of reference setpoints, an H-infinity (optimal) feedback controller is designed. Actually, the proposed H-infinity controller for the model of the two-link electropneumatically actuated exoskeleton achieves the solution of the associated optimal control problem under model uncertainty and external disturbances. This controller implements a min-max differential game taking place between: (i) the control inputs which try to minimize a cost function which comprises a quadratic term of the state vector’s tracking error and (ii) the model uncertainty and perturbation inputs which try to maximize this cost function. To select the stabilizing feedback gains of this H-infinity controller, an algebraic Riccati equation is being repetitively solved at each time-step of the control method. The global stability properties of the H-infinity control scheme are proven through Lyapunov analysis.

Pneumatic actuators are characterized by high nonlinearities which are due to air compressibility, thermodynamics and valves behavior and thus pneumatic robots require elaborated nonlinear control schemes to ensure their fast and precise positioning. Among the control methods which have been applied to pneumatic robots, one can distinguish differential geometric approaches (Lie algebra-based control, differential flatness theory-based control, nonlinear model predictive control [NMPC], sliding-mode control, backstepping control and multiple models-based fuzzy control). Treating nonlinearities and fault tolerance issues in the control problem of robotic manipulators with electropneumatic actuators has been a nontrivial task.

The novelty of the proposed control method is outlined as follows: preceding results on the use of H-infinity control to nonlinear dynamical systems were limited to the case of affine-in-the-input systems with drift-only dynamics. These results considered that the control inputs gain matrix is not dependent on the values of the system’s state vector. Moreover, in these approaches the linearization was performed around points of the desirable trajectory, whereas in the present paper’s control method the linearization points are related with the value of the state vector at each sampling instance as well as with the last sampled value of the control inputs vector. The Riccati equation which has been proposed for computing the feedback gains of the controller is novel, so is the presented global stability proof through Lyapunov analysis. This paper’s scientific contribution is summarized as follows: (i) the presented nonlinear optimal control method has improved or equally satisfactory performance when compared against other nonlinear control schemes that one can consider for the dynamic model of robots with electropneumatic actuators (such as Lie algebra-based control, differential flatness theory-based control, nonlinear model-based predictive control, sliding-mode control and backstepping control), (ii) it achieves fast and accurate tracking of all reference setpoints, (iii) despite strong nonlinearities in the dynamic model of the robot, it keeps moderate the variations of the control inputs and (iv) unlike the aforementioned alternative control approaches, this paper’s method is the only one that achieves solution of the optimal control problem for electropneumatic robots.

The use of electropneumatic actuation in robots exhibits certain advantages. These can be the improved weight-to-power ratio, the lower mechanical impedance and the avoidance of overheating. At the same time, precise positioning and accurate execution of tasks by electropneumatic robots requires the application of elaborated nonlinear control methods. In this paper, a new nonlinear optimal control method has been developed for electropneumatically actuated robots and has been specifically applied to the dynamic model of a two-link robotic exoskeleton. The benefit from using this paper’s results in industrial and biomedical applications is apparent.

A comparison of the proposed nonlinear optimal (H-infinity) control method against other linear and nonlinear control schemes for electropneumatically actuated robots shows the following: (1) Unlike global linearization-based control approaches, such as Lie algebra-based control and differential flatness theory-based control, the optimal control approach does not rely on complicated transformations (diffeomorphisms) of the system’s state variables. Besides, the computed control inputs are applied directly on the initial nonlinear model of the electropneumatic robot and not on its linearized equivalent. The inverse transformations which are met in global linearization-based control are avoided and consequently one does not come against the related singularity problems. (2) Unlike model predictive control (MPC) and NMPC, the proposed control method is of proven global stability. It is known that MPC is a linear control approach that if applied to the nonlinear dynamics of the electropneumatic robot, the stability of the control loop will be lost. Besides, in NMPC the convergence of its iterative search for an optimum depends on initialization and parameter values selection and consequently the global stability of this control method cannot be always assured. (3) Unlike sliding-mode control and backstepping control, the proposed optimal control method does not require the state-space description of the system to be found in a specific form. About sliding-mode control, it is known that when the controlled system is not found in the input-output linearized form the definition of the sliding surface can be an intuitive procedure. About backstepping control, it is known that it cannot be directly applied to a dynamical system if the related state-space model is not found in the triangular (backstepping integral) form. (4) Unlike PID control, the proposed nonlinear optimal control method is of proven global stability, the selection of the controller’s parameters does not rely on a heuristic tuning procedure, and the stability of the control loop is assured in the case of changes of operating points. (5) Unlike multiple local models-based control, the nonlinear optimal control method uses only one linearization point and needs the solution of only one Riccati equation so as to compute the stabilizing feedback gains of the controller. Consequently, in terms of computation load the proposed control method for the electropneumatic actuator’s dynamics is much more efficient.

The purpose of this paper is to address the synthesis and experimental application of a generalized predictive control (GPC) technique on an Orthoglide robot.

The control strategy is composed of two control loops. The inner loop aims at linearizing the nonlinear robot dynamics using feedback linearization. The outer loop tracks the desired trajectory based on GPC strategy, which is robustified against measurement noise and neglected dynamics using Youla parameterization.

The experimental results show the benefits of the robustified predictive control strategy on the dynamical performance of the Orthoglide robot in terms of tracking accuracy, disturbance rejection, attenuation of noise acting on the control signal and parameter variation without increasing the computational complexity.

The paper shows the implementation of the robustified predictive control strategy in real time with low computational complexity on the Orthoglide robot.

This paper aims to present novel results for trajectory tracking of tandem-rotor helicopters via variance-constrained controllers.

Regarding these purposes, linearized tandem-rotor helicopter models are benefitted.

Variance-constrained controllers are very beneficial for trajectory tracking of tandem-rotor helicopters while there exists variance bounds on outputs of interest.

Variance-constrained controllers can be used for cheaper tandem-rotor helicopter operations with high trajectory tracking quality.

Applying variance-constrained control strategy for tandem-rotor helicopters during trajectory tracking. This also causes less fuel consumption and green environment, and good trajectory tracking quality.