The adaptive sliding mode control based on U–K theory for foot trajectory following of hexapod robot

This paper provides an adaptive robust control strategy for foot trajectory following control of hexapod robot on basis of the Udwadia–Kalaba theory. In this paper, the foot trajectory following control problem of the hexapod robot is transformed into the problem of solving the system control constraint force on basis of the Udwadia–Kalaba theory. Compared with the traditional control strategy, linearization or approximations are not required by using the Udwadia–Kalaba theory for nonlinear system such as the hexapod robot. Due to modeling error, measurement error and the change of working state, the system may have non-ideal initial conditions, vibration interference and other uncertain factors during operation, which affect the control accuracy. An adaptive robust controller is designed for solving uncertainties. Meanwhile, the stability is analyzed by using the second method of Lyapunov function. Finally, the accuracy and stability of the control method proposed are verified by establishing the leg model of the hexapod robot and conducting simulation analysis. The simulation results show that the provided adaptive control process has faster error convergence speed and response speed compared with the sliding mode control method.

In modern vehicles, electronic throttle &#x0028 ET &#x0029 has been widely utilized to control the airflow into gasoline engine. To solve the control difficulties with an ET, such as strong nonlinearity, unknown model parameters and input saturation constraints, an adaptive sliding-mode tracking control strategy for an ET is presented. Compared with the existing control strategies for an ET, input saturation constraints and parameter uncertainties are adequately considered in the proposed control strategy. At first, the nonlinear dynamic model for control of an ET is described. According to the dynamical model, the nonlinear adaptive sliding-mode tracking control method is presented, where parameter adaptive laws and auxiliary design system are employed. Parameter adaptive law is given to estimate the unknown parameter with an ET. An auxiliary system is designed, and its state is utilized in the tracking control method to handle the input saturation. Stability proof and analysis of the adaptive sliding-mode control method is performed by using Lyapunov stability theory. Finally, the reliability and feasibility of the proposed control strategy are evaluated by computer simulation. Simulation research shows that the proposed sliding-mode control strategy can provide good control performance for an ET.

To improve the trajectory tracking control of the robotic fish driven by four-joint tail fins, the paper has established the dynamic model of four-joint tail fins on Udwadia-Kalaba theory and designed a sliding mode controller for trajectory tracking. Meanwhile, the stability of the robotic fish has been analyzed and discussed. A comparative study of the sliding mode controller and PID controller has been conducted on numerical simulation experiments. The results show the effectiveness and accuracy of the proposed control strategy. Compared with the PID controller, the sliding mode controller can converge to the desired value relatively quickly.

It's difficult for pneumatic actuator systems to fit into an accurate dynamic model for model-based sliding-mode control design because of the nonlinear and time-varying characteristics. The objective of this research is to develop a new H(subscript ∞) tracking-based adaptive sliding-mode controller for nonlinear pneumatic actuator systems. The controller initially uses a Fourier series-based functional approximation to reach an unknown function so as to circumvent the prerequisites of the models. The H(subscript ∞) tracking technique can then be incorporated into an adaptive sliding-mode control method to protect the derived controller from approximated errors, un-modeled dynamics and disturbances. Thus, system dynamic models are not necessary for achieving the proposed controller design with H(subscript ∞) tracking performance and trial-and-error is not required to select an approximation function. System stability is ensured through the new laws for the coefficients of the Fourier-series functions which are derived from a Lyapunov function. In addition, the serious chattering problem can be reduced through the projected H(subscript∞)tracking-based adaptive sliding-mode controller control method by means of the H(subscript∞) tracking controller in comparison with the Fourier series-based adaptive sliding-mode controller. Consequently, the practical experiments on a rodless pneumatic servo system are successfully implemented with different path tracking profiles, which validates the proposed method.

This paper presents a control strategy for a 4Y octocopter aircraft that is influenced by multiple actuator faults and external disturbances. The approach relies on a disturbance observer, adaptive type-2 fuzzy sliding mode control scheme, and type-1 fuzzy inference system. The proposed control approach is distinct from other tactics for controlling unmanned aerial vehicles because it can simultaneously compensate for actuator faults and external disturbances. The suggested control technique incorporates adaptive control parameters in both continuous and discontinuous control components. This enables the production of appropriate control signals to manage actuator faults and parametric uncertainties without relying only on the robust discontinuous control approach of sliding mode control. Additionally, a type-1 fuzzy logic system is used to build a fuzzy hitting control law to eliminate the occurrence of chattering phenomena on the integral sliding mode control. In addition, in order to keep the discontinuous control gain in sliding mode control at a small value, a nonlinear disturbance observer is constructed and integrated to mitigate the influence of external disturbances. Moreover, stability analysis of the proposed control method using Lyapunov theory showcases its potential to uphold system tracking performance and minimize tracking errors under specified conditions. The simulation results demonstrate that the proposed control strategy can significantly reduce the chattering effect and provide accurate trajectory tracking in the presence of actuator faults. Furthermore, the efficacy of the recommended control strategy is shown by comparative simulation results of 4Y octocopter under different failing and uncertain settings.

Introduction. This study presents a robust control method for the path following problem of the PUMA560 robot. The technique is based on the Adaptive Fuzzy Type-2 Fast Terminal Sliding Mode Control (AFT2FTSMC) algorithm and is designed to handle actuator faults, uncertainties (such as payload change), and external disturbances. The aim of this study is to utilize the Fast Terminal Sliding Mode Control (FTSMC) approach in order to ensure effective compensation for faults and uncertainties, minimize tracking error, reduce the occurrence of chattering phenomena, and achieve rapid transient response. A novel adaptive fault tolerant Sliding Mode Control (SMC) approach is developed to address the challenges provided by uncertainties and actuator defects in real robotics tasks. Originality. The present work combined the AFT2FTSMC algorithm in order to give robust controllers for trajectory tracking of manipulator’s robot in presence parameters uncertainties, external disturbance, and faults. We use an adaptive fuzzy logic system to estimate the robot’s time-varying, nonlinear, and unfamiliar dynamics. A strong adaptive term is created to counteract actuator defects and approximation errors while also guaranteeing the convergence and stability of the entire robot control system. Novelty. The implemented controller effectively mitigates the chattering problem while maintaining the tracking precision and robustness of the system. The stability analysis has been conducted using the Lyapunov approach. Results. Numerical simulation and capability comparison with other control strategies show the effectiveness of the developed control algorithm. References 53, table 1, figures 8.

ABSTRACTA robust approximate constraint‐following control (RACC) approach is proposed in this article for collaborative robots with inequality constraints. The trajectory‐following control and boundary control of the robot are investigated. First, an explicit constraint equation for the collaborative robot system is established based on the Udwadia–Kalaba (U‐K) theory. Second, due to the monotone unbounded property of the tangent function, a special function is constructed to transform the joint output angles of the constrained robot into unconstrained state variables, and a new form of the robot constraint equation is obtained. Through this transformation, the joint motion of the robot will always be confined to specified angles and follow the desired trajectory. The constraint equation ensures the safety of the robot at the algorithmic level and innovatively solves the control problem of the equality and inequality of the robot's motion. According to theoretical analysis, the control approach can deal with uncertainty and satisfy both uniform boundedness (UB) and uniform ultimate boundedness (UUB) requirements. Finally, based on the rapid controller prototype CSPACE and a two‐degree‐of‐freedom collaborative robot platform, experimental verification is carried out. Numerical simulation and experimental results demonstrate that the proposed RACC approach with state transformation exhibits significant advantages in trajectory tracking performance and safety for collaborative robots.

This paper presents an adaptive sliding mode controller (ASMC) with the implication of a forgetting factor for a two-degree-of-freedom (2-DOF) arm robot manipulator trajectory tracking. The proposed approach builds upon conventional sliding mode control (SMC), which is well known for its robustness and low tracking error. The controller dynamically adjusts this parameter by introducing an adaptive mechanism to enhance trajectory tracking, guarantee high robustness, and reduce chattering effects. In order to mitigate gain drift, a forgetting factor is incorporated into the adaptation law, ensuring stable and reliable control performance. Stability is validated using Lyapunov theory, and the effectiveness of the proposed ASMC is evaluated through numerical simulations. The simulations are conducted in MATLAB R2023b using a dynamic model of the 2-DOF robotic manipulator. Comparative results with conventional SMC confirm that the adaptive approach significantly improves tracking accuracy, noise robustness, and chattering suppression.

This article proposed a novel approach for the dynamic modeling and controller design of a passive-wheel snake robot based on Udwadia–Kalaba theory. Compared to common methods, this approach is easily processed for many-degree-of-freedom snake robot. The desired trajectory is easily modeled as a trajectory constraint, and the nonholonomic constraints from the passive wheels’ lateral velocity are also easily handled using Udwadia–Kalaba theory. Besides the proposed equation of motion is analytical, no approximation or linearization as well as extra variables such as Lagrangian multiplier is needed as common methods usually do. The servo joint constraint forces are precisely calculated by solving Udwadia–Kalaba equation, and no complicated control structure design is needed as common control methods always do especially for under-actuated mechanical systems. This article provides a novel dynamic modeling and controller design approach for the passive-wheel snake robot in a new perspective. The theoretical analysis and simulation verify the proposed approach. The trajectory has good incidence with the designed one, and the real-time joint forces are also conveniently acquired.

This paper develops a novel adaptive fuzzy sliding mode controller for the diving control of autonomous underwater vehicle (AUV). Unlike most previous AUVs’ control approaches, in this paper, the problem of input saturation constraint of rudder angle is considered, and the new auxiliary systems are proposed. Considering the modeling uncertainty of the dynamic model, an adaptive sliding mode controller based on fuzzy logic system is proposed, and the new update laws of control parameters are given. For the adaptive sliding mode controller design, although the input gain of each subsystem is partially known, only one fuzzy logic system is needed for online identification, which is a distinct difference from the previous adaptive sliding mode controllers. The uniformly ultimately boundedness of tracking error is proven by Lyapunov theorem. The effectiveness of the proposed control scheme is illustrated by simulation.

This paper proposes and evaluates a novel control approach for trajectory tracking, stability enhancement, and vibration reduction of a flexible joint robot (FJR). The FJR is a 2-degree-of-freedom underactuated nonlinear system that is challenging to control due to vibration, underactuation, uncertainties, and external disturbances. The control objectives are high trajectory tracking performance together with suppressing vibration. The proposed control approach uses integral sliding mode control (ISMC) combined with a barrier function based on back-stepping. This ensures robust and smooth performance by eliminating the reaching phase where sliding mode control (SMC) is typically not robust. Robustness is thus guaranteed from the start. The FJR is modeled as a 4th-order system using Lagrangian mechanics and decomposed into two 2nd-order subsystems for control design. Sliding variables are defined for each subsystem. Using these variables, the proposed control achieves robust trajectory tracking, stability, and vibration reduction. Numerical simulations in MATLAB validate the superior performance of the proposed ISMC-barrier function control compared to conventional ISMC for the FJR. This novel control approach addresses the challenges of controlling this FJR.

Purpose In this paper, an adaptive fuzzy sliding mode controller (AFSMC) is developed for the formation control of a team of autonomous underwater vehicles (AUVs) subjected to unknown payload mass variations during their mission. Design/methodology/approach A sliding mode controller (SMC) is designed to drive the state trajectories of the AUVs to a switching surface in the state space. The payload mass variation results in parameter variation in AUV dynamics leading to actuator failure. This further leads to loss of communication among the members of the team. Hence, an adaptive SMC based on fuzzy logic is developed to maintain the coordinated motion of AUVs with payload mass variation. Findings The results are obtained by employing adaptive SMC for AUVs with and without payload variations and are compared. It is observed that the proposed adaptive SMC exhibits improved performance and tracks the desired trajectory in less time even with variation in the payload. The adaptive fuzzy control algorithm is developed to handle variation in payload mass variation. Lyapunov theory is used to establish stability of AFSMC controller. Research limitations/implications Perfect alignment is assumed between centres of gravity (OG) and buoyancy (OB), thus AUVs maintaining horizontal stability during motion. The AUVs’ body centres are aligned with centres of gravity (OG), thus the distance vector being rg = [0,0,0]T. As it is a tracking problem, sway motion cannot be neglected as the AUVs are travelling in a curved locus, hence susceptible to Coriolis and centripetal forces. The AUV is underactuated as only two thrusters at the stern plate that are employed for the surge and yaw controls and error in Y- direction are controlled by adjusting control input in surge and heave direction. Control inputs to the thruster are constants, and depth control is achieved by adjusting the rudder angle. Practical implications AUVs are employed in military mission or surveys, and they carry heavy weapons or instrument to be deployed at or picked from specific locations. Such tasks lead to variation in payload, causing overall mass variation during an AUV’s motion. A sudden change in the mass after an AUV release or pick load results in variation in depth and average velocity. Social implications The proposed controller can be useful for military missions for carrying warfare and hydrographic surveys for deploying instruments. Originality/value A proposed non-linear SMC has been designed, and its performances have been verified in terms of tracking error in X, Y and Z directions. An adaptive fuzzy SMC has been modelled using quantized state information to compensate payload variation. The stability of AFSMC controller is established by using Lyapunov theorem, and reachability of the sliding surface is ensured.

Event-triggered adaptive deep neural network sliding mode control design for unmanned aerial vehicle systems

Adaptive Higher Order Sliding Mode Control for Nonlinear Uncertain Systems

The high accuracy tracking control of multi-axis manipulator with uncertainty is always a difficult problem for control theorists and engineers. The Udwadia–Kalaba theory effectively characterizes the explicit dynamics equations of constrained mechanical systems. The Sliding Mode Control (SMC) law is implemented under the circumstance of uncertainties in manipulator model, fluctuations in parameters, and external disturbances. However, the existing SMC law has limitations in the convergence speed and chattering. A proposed SMC law combining nonlinear sliding mode hypersurface and double-power reaching law is presented on the basis of dynamic equation provided by the Udwadia–Kalaba theory, which can address the slow convergence speed of reaching law and chattering phenomenon of SMC dynamic response. Moreover, the superiority of the proposed SMC law is verified through a comparison with two compared SMC laws: one that integrates a linear sliding mode manifold with an exponential reaching law, and another that combines the linear sliding mode manifold with the double-power reaching law. Finally, taking the SCARA robot as an illustrative example, the proposed scheme is implemented to the constraint tracking control of the multi-axis manipulator. The results show that the system has stronger robustness and faster convergence speed, which verifies the convincingness of the proposed strategy.