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New technological advances are changing the way robotics are designed for safe and dependable physical human–robot interaction and human-like prosthesis. Outstanding examples are the adoption of soft covers, compliant transmission elements, and motion control laws that allow compliant behavior in the event of collisions while preserving accuracy and performance during motion in free space. In this scenario, there is growing interest in variable stiffness actuators (VSAs). Herein, we present a new design of an anthropomorphic elbow VSA based on an architecture we developed previously. A robust dynamic feedback linearization algorithm is used to achieve simultaneous control of the output link position and stiffness. This actuation system makes use of two compliant transmission elements, characterized by a nonlinear relation between deflection and applied torque. Static feedback control algorithms have been proposed in literature considering purely elastic transmission; however, viscoelasticity is often observed in practice. This phenomenon may harm the performance of static feedback linearization algorithms, particularly in the case of trajectory tracking. To overcome this limitation, we propose a dynamic feedback linearization algorithm that explicitly considers the viscoelasticity of the transmission elements, and validate it through simulations and experimental studies. The results are compared with the static feedback case to showcase the improvement in trajectory tracking, even in the case of parameter uncertainty.

Traditional input–output feedback linearization requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system’s uncertainties. In this paper, a model-free active input–output feedback linearization technique based on an improved active disturbance rejection control paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with a known relative degree. The linearization control law is composed of a scaled generalized disturbance estimated by an improved nonlinear extended state observer with saturation-like behavior and the nominal control signal produced by an improved nonlinear state error feedback. The proposed active input–output feedback linearization cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, which is the only information required about the nonlinear system. Stability analysis has been conducted based on the Lyapunov functions and revealed the convergence of the improved nonlinear extended state observer and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed active input–output feedback linearization technique on the single-link flexible joint manipulator. The simulations results validated the effectiveness of the proposed active input–output feedback linearization tool based on improved active disturbance rejection control as compared to the conventional active disturbance rejection control–based active input–output feedback linearization and the traditional input–output feedback linearization techniques.

This paper presents the trajectory tracking control design and implementation of feedback linearization (FL) and robust feedback linearization (RFL), applicable to a robotic lawnmower with four mecanum driving wheels. The RFL control design additionally includes a robust control law. These two nonlinear control laws are developed to enable the controlled robotic lawnmower to accurately follow any specified trajectory. The simulation outcomes illustrate that the suggested control law based on RFL displays superior trajectory tracking accuracy and resilience compared to the FL control method in the case of a robotic lawnmower operating under demanding conditions. These conditions encompass environmental disturbances and uncertainties in modeling. The RFL control method also exhibits lower energy consumption compared to the FL control method. Finally, using the RFL controller derived from this study, the error in trajectory tracking in computer simulations and the actual mowing performance have demonstrated outstanding results.

In this research, a robust feedback linearization technique is analysed for robot manipulators control. A complete first-order Taylor series expansion is used to linearize the robot dynamics which takes into account initial conditions and the Taylor-series remainder. A modified PD control law with Taylor-series compensation is used to guarantee robust reference tracking. Whilst classic feedback linearization controllers guarantee asymptotic convergence to zero, the proposed approach shows that, for real applications, if the linearized robot dynamics is stable then the nonlinear robot states are also stable and remain bounded. This premise is assessed via Lyapunov stability theory under a controllability and observability analysis; and hence, exponential convergence to a bounded set is concluded. Experiments are carried out using a 1-degree of freedom robot and a 4-degree of freedom exoskeleton robot to validate the proposed approach.

The turntable plays an important role in semi-physical simulation of missiles and other aircraft. The precision of its control directly influences aircraft performance. However, the inertial coupling among the three-axis frames of the turntable limits the enhancement of tracking accuracy. This paper establishes a three-axis turntable model, hydraulic model, friction torque model, and gravity torque model, and then obtains expressions for inertial coupling and torque coupling. Based on this, a feedback linearization controller for hydraulic flight simulation turntable is designed with variable inertia model compensation. Finally, through comparative experiments, effectiveness and practicality of proposed control method are verified. Specifically, the proposed control method reduced the average tracking error of the turntable by 18.35% compared to traditional control methods, demonstrating its promising application prospects.

Effective communication between multiple autonomous underwater vehicles (AUVs) is necessary for formation control. As the most reliable underwater communication method, acoustic communication still has many constraints compared with radio communication, which affects the effectiveness of formation control. Therefore, this paper proposes a formation control scheme for multiple AUVs under communication delay, packet discreteness and dropout. Firstly, the communication delay is estimated based on the kernel density estimation method. To solve the problem of packet discreteness and dropout, the curve fitting method is used to predict the states of the AUV. Secondly, a follower controller is designed based on the leader–follower approach using input–output feedback linearization, which is proven to be stable with Lyapunov stability theory. Then, some simulation results are presented to demonstrate the stability and accuracy of the formation control in different communication environments. Finally, the field tests on the lake show that the scheme introduced in this paper is valid and practical.

In this paper, we propose a new class nonlinear hybrid controller (NHC) for swinging-up and stabilizing the (under-actuated) rotary inverted pendulum system. First, the swing-up controller, which drives the pendulum up towards the desired upright position, is designed based on the feedback linearization and energy control methods. Then, the modified super-twisting sliding mode control is proposed based on the new sliding surface to stabilize both the fully-actuated (the rotary arm) and under-actuated (the pendulum) state variables. In the proposed NHC, around the upright position, the stabilization controller is applied, and in different circumstances aside from the upright position, the swing-up controller is used. We show that with the proposed NHC: (i) in the swing-up stage, the pendulum is able to reach the desired upright position; and (ii) in the stabilization stage, the closed-loop rotary inverted pendulum is asymptotically stable. We demonstrate the effectiveness of the proposed NHC through extensive experiments. In particular, (i) the faster swing-up under the similar control effort is obtained, compared with the existing fuzzy logic swing-up controller; (ii) the better stabilization control performance for the convergence of the angular positions of the rotary arm and pendulum is attained and the chattering is alleviated, compared with the existing sliding mode stabilization controllers; (iii) the better stabilization control accuracy with the faster convergence time and lower peak overshoot is accomplished, compared with the existing Fuzzy-LQR controller; and (iv) the good robustness against sudden external disturbances is achieved.

This work proposes a novel method for the real-time identification and nonlinear control of a permanent-magnet synchronous motor (PMSM) based on a Physics-Informed Neural Network (PINN) and the exact feedback linearization approach. The proposed approach is presented in a direct-quadrature framework, where the quadrature current and the rotational speed are selected as outputs and the direct and quadrature voltages are selected as inputs. A nonlinear difference equation is selected to describe the physical dynamics of the PMSM, and a PINN is designed based on the aforementioned structure. A simplified training scheme is designed for the PINN based on a least-squares structure to facilitate online training in real time. A nonlinear controller based on exact feedback linearization is designed by considering the nonlinear model of the system identified based on the PINN. Therefore, the proposed approach involves identification and control in real time, where the PINN is trained online. In order to track the reference for the rotational speed, a nonlinear controller with integral action based on exact feedback linearization is designed based on a linear quadratic regulator. As a result, the proposed approach can be used to identify the system to be controlled in real time, and it is able to track any small change in the real model; in addition, it is robust to both external and internal disturbances, such as variations in torque load and resistance. The proposed approach is evaluated through simulation and using a real PMSM, and the results of reference tracking are evaluated under disturbances. The identification performance is evaluated by using a Taylor diagram under closed-loop and open-loop structures, where ARX and NARX structures are used for comparison. It is thereby verified that this novel proposed control approach involving a PINN-based model can adequately track the dynamics of a PMSM system, where the performance of the proposed nonlinear control is maintained even when using the identified model based on the PINN.

Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback linearizability obtained. Additionally, a systematic procedure for obtaining all the smooth, generic system trajectories is shown to follow from the theory. Besides smoothness and the existence of symmetry, no further assumption is made on the local form of a control system, which is therefore permitted to be fully nonlinear and time varying. Likewise, no constraints are imposed on the local form of the dynamic compensator. Particular attention is given to the consideration of geometric (coordinate independent) structures associated to control systems with symmetry. To show how the theory is applied in practice we work through illustrative examples of control systems, including the vertical take-off and landing system, demonstrating the significant role that Lie symmetry plays in dynamic feedback linearization. Besides these, a number of more elementary pedagogical examples are discussed as an aid to reading the paper. The constructions have been automated in the Maple package DifferentialGeometry.

The aim of this study is to investigate nonlinear DC motor behavior and to control velocity as output variable. The linear model is designed, but as it is experimentally verified that it does not describe the system well enough it is replaced by the nonlinear one. System’s model has been obtained taking into account Coulomb and viscous friction in the firmly nonlinear environment. In the frame of the paper the dynamical analysis of the nonlinear feedback linearizing control is carried out. Furthermore, a metaheuristic optimization algorithm is set up for finding the coefficient of the proportional-integral feedback linearizing controller. For this purpose Gray wolf optimization technique is used. Moreover, after the introduction of the control law, analysis of the pole placement and stability of the system is establish. Optimized nonlinear control signal has been applied to the real object with simulated white noise and step signal as disturbances. Finally, for several desired output signals, responses with and without disruption are compared to illustrate the approach proposed in the paper. Experimental results obtained on the given system are provided and they verify nonlinear control robustness.