Aug 2026· Journal of Vibration and Control· 0 citations· 18 references
TL;DR
The potential of the proposed Adaptive Dynamic Programming (ADP) framework for improving trajectory-tracking performance in spherical robots under uncertain operating conditions is demonstrated.
Abstract
Controlling spherical robots is challenging due to their nonlinear dynamics, underactuated characteristics, and non-holonomic constraints. These challenges become more pronounced in the presence of parameter variations and external disturbances. To address these issues, this paper proposes an Adaptive Dynamic Programming (ADP)-based control framework for spherical robot dynamics. The stability properties of the proposed method are analyzed using Lyapunov theory. The kinematic control layer is designed based on the feedback linearization approach, while the dynamic controller employs ADP to compensate for uncertainties and disturbances. The effectiveness of the proposed method is evaluated through two simulation case studies involving trajectory-tracking tasks under parametric uncertainties and external disturbances. The simulation results show that the proposed controller is capable of achieving accurate trajectory tracking while maintaining stable system performance. To provide a comparative assessment, a Sliding Mode Control (SMC) scheme is also implemented under the same conditions. The obtained results indicate that the ADP-based controller can reduce tracking errors and power consumption compared with the considered SMC approach. In one case study, the tracking error integral achieved by the ADP controller is approximately 36% lower than that of SMC, while the corresponding power consumption is reduced by about 23%. These results demonstrate the potential of the proposed ADP framework for improving trajectory-tracking performance in spherical robots under uncertain operating conditions.
Accurate trajectory tracking is a fundamental requirement for autonomous mobile robots (AMRs) operating in complex environments. This paper addresses the tracking control problem for AMRs subject to kinematic constraints. A linearized model predictive control (LMPC) framework is proposed to effectively reduce trajectory tracking errors while ensuring smooth control inputs and high computational efficiency. First, the nonlinear kinematic model of the robot is derived and linearized around the reference trajectory using Taylor series expansion to obtain a discrete-time linear error dynamic model. Second, the tracking problem is formulated as a constrained finite-horizon optimization problem, which is transformed into a standard quadratic programming (QP) form to guarantee computational efficiency. Extensive simulations are conducted using a complex butterfly-shaped trajectory characterized by continuous curvature variations. The results demonstrate that the proposed controller achieves high tracking accuracy with centimeter-level position errors and generates feasible control inputs that strictly satisfy constraints, thereby demonstrating the robustness and effectiveness of the proposed controller.
Song-Ling Yu· International Conference on...· 0 citations
In this paper, a robust control method is suggested for attitude control of the two-wheeled self-balancing robot by combining feedback linearization with sliding mode control techniques. The proposed method takes into account important challenges such as external disturbance and system uncertainty. Feedback linearization cancels the nonlinearities in the dynamics of the robotic system, while the sliding mode control handles the uncertainties and the external disturbance. The parameters of the proposed controller are selected by tuning the controller with the Atom Search Optimization algorithm. MATLAB is used to simulate the proposed controller. Simulation results indicate a good performance of the presented controller with high robustness compared with the proportional-integral-derivative (PID) controller. Moreover, the proposed method reduces the rise time by approximately 40% and 50% with respect to PID. These results illustrate the feasibility of the presented control method to be used for real-time implementation in autonomous robotic balancing systems.
Alaa Jumaah Al-Maiahy, Y. Khidhir, A. J. Attiya et al.· IAES International Journal o...· 0 citations
The trajectory tracking control problem of multi-degree-of-freedom robotic manipulators ((DOF-RM) has attracted widespread attention due to inherent challenges, including nonlinearity, parameter uncertainty, and unknown external disturbances. This paper proposes a robust trajectory tracking control scheme utilizing linear extended state observer (LESO). First, a dynamic model of the robotic manipulator is established, and all unmodeled dynamics and exogenous perturbations are merged into a lumped disturbance term. Second, a parameterized high-gain LESO is designed for realtime estimation of the system state and lumped disturbances, the designed observer only requires the adjustment of a single bandwidth parameter. Finally, the LESO is combined with a robust tracking controller to design an active disturbance-resistant tracking controller. Rigorous stability proofs using Lyapunov stability theory demonstrate that the tracking error and the observer estimation error are uniformly and eventually bounded. Finally, numerical simulations of a two-DOF robotic arm verify the tracking performance of the proposed method.
Hua-Ran Wang· International Conference on...· 0 citations
This work introduces a Model Predictive Control (MPC) path tracking controller, which is developed to boost robustness, tracking precision, and vehicle stability when navigating high-speed and high-curvature driving scenarios. First, a 3-degree-of-freedom (3-DOF) dynamic model of the vehicle is established to serve as a reference. Next, a linear time-varying MPC control algorithm is formulated, with constraints on yaw rate, lateral velocity, and road boundary conditions taken into account; a comprehensive performance metric that balances tracking accuracy and control smoothness is also defined. Third, the time-domain parameters of the MPC framework are optimized using an improved genetic algorithm. Finally, the effectiveness and accuracy of the proposed controller are validated via co-simulation experiments conducted on the Matlab/Simulink and Carsim platforms. Simulation results demonstrate that the controller exhibits excellent robustness: the peak lateral tracking error is only 0.05 m on high-friction roads and 0.12 m on low-friction roads, with a maximum heading error of 0.15°. Additionally, the vehicle’s dynamic stability is notably enhanced: the yaw rate is reduced by 9.6% and 15.7% on high- and low-adhesion roads, respectively, while the sideslip angle is decreased by 13.2% and 18.4% under the same conditions.
Hanzhengnan Yu, Xiao-Yi Hou, Hao Zhang et al.· SAE technical paper series· 0 citations
With the rapid development of modern industry, robotic manipulators are required to achieve increasingly high trajectory-tracking accuracy and robustness in practical applications. To enhance tracking performance under complex operating conditions, this paper proposes an Adaptive Model Predictive Control with Sliding-Mode Robust Compensation (AMPC–SMC) scheme that integrates an adaptive mechanism with sliding-mode control theory. First, a dynamic model of the manipulator is established, and parameter linearization is employed to transform the nonlinear dynamics into a linearly parameterized form with unknown parameters. Second, an adaptive law is derived based on Lyapunov stability theory to update the model parameters online, thereby mitigating the adverse effects of parametric perturbations and external disturbances on tracking accuracy. Building on this, a receding-horizon optimization strategy is introduced by formulating a quadratic cost function that penalizes both tracking errors and control effort, and the optimal control input is obtained by solving the resulting optimization problem. Meanwhile, a sliding-mode term is incorporated as a robust compensator to eliminate residual tracking errors. Finally, the desired trajectory is generated via point-to-point path planning in Cartesian space, and the proposed method is validated on a real six-degree-of-freedom robotic manipulator. Comparative experiments against conventional model predictive control (MPC) and traditional sliding-mode control (SMC) demonstrate that the proposed AMPC-SMC controller achieves remarkably superior tracking performance compared with the conventional MPC and SMC controllers. In terms of tracking accuracy, the mean absolute errors (MAE) of Joint 2, Joint 4 and Joint 5 under AMPC-SMC are reduced by 91.7%, 92.1% and 86.1% respectively relative to MPC, and decreased by 76.1%, 77.3% and 85.1% compared with the standalone SMC controller.
Zhonggang Xiong, Deqing Liu, Mengyi Li et al.· Symmetry· 0 citations
This study presents an adaptive sliding mode control approach for trajectory tracking of a quadrotor unmanned aerial vehicle functioning under external interference and kinematic unpredictability. Linear and rotational motion equations formulated in inactive local coordinate system frames are developed with the aid of a nonlinear six-degrees-of-freedom quadrotor dynamic model. Through mitigating excessive switching activity, reliability is improved. Here, the proposed controller integrates sliding mode control with bounded adaptive switching gain factors and boundary-layer smoothing. The operational design is applied within a sequential outer-loop/inner-loop structure for linear and orientation control. The conventional sliding mode control, alongside the proportional derivative control, which employs MATLAB/Simulink R2024a simulations while being interference-affected with an unknown performance set-up, is deployed in this work to relatively appraise the proposed ASM controller. The assessment involves three-dimensional trajectory, control input characteristics, tracking error analysis, adaptive gain growth, and chattering analysis with quantitative performance metrics. The computational output revealed that the proposed ASMC attained superior tracking performance with limited oscillation and level control action. The controller achieves a total RMSE of approximately 0.38 m and a lower aggregate tracking error when using the conventional SMC and PD controllers under equivalent conditions. Furthermore, the adaptive gain mechanism successfully lowers chattering while maintaining robustness against interferences, a large amount of ambiguity, and inertial imbalance with signal noise. The results validate that the proposed ASMC delivers a functional balance between robustness, control smoothness, and tracking accuracy alongside execution homogeneity for autonomous quadrotor UAV trajectory tracking in unsettled and unstable environments.
Muktar Fatihu Hamza· Automation· 0 citations
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