🤖 Duc-Cuong VU, BSc.

The operation of waves, winds, and ocean currents that affect ships or marine vehicles poses a number of challenges for systems that require balance. To address this issue, this study introduces a 6-degree-of-freedom parallel robot Stewart platform erected on the ship deck to isolate vibrations. First, Lagrangian-based modeling is applied to the ship-mounted Stewart platform. Unlike previous systems that are based on Kane’s method or Newtonian mechanics, the Lagrangian-based approach does not require a large number of tedious mathematical transformations; instead, it can be generated by a computer. Because of the complexity of the simulation model, the control design model is simplified from the original. Following that, the Control Lyapunov Function (CLF) is employed to achieve zero convergence and the stabilization of the state errors. To ensure operational safety, the Quadratic Program (QP) problem takes into account the Control Barrier Function (CBF) and Exponential Control Barrier Function (ECBF) constraints. The controllers are equipped with High-Gain Disturbance Observation (DOB). Finally, the Lagrangian-based model is validated by comparison with the MATLAB Simscape Multibody platform. In addition, the performance of the proposed control strategies is analyzed.

This study investigates an automatic navigation method for one type of underactuated system, ball-balancing robot (ballbot), in complex environments with both dynamic obstacles and complex-shaped obstacles. To ensure safe operations, which means that ballbot has to avoid obstacles and maintain tilt angles in a desired range, Nonlinear Model Predictive Control (NMPC) is formulated to predict the position and behavior of the ballbot, followed by the optimization problem assisted by Control Barrier Function (CBF) constraints to drive the ballbot in the safe trajectory. Instead of directly implementing tilt angle limitations on the main NMPC, another Quadratic Programming Optimizer based on CBF is designed outside the main controller to reduce the constraint complexity of optimization. An elliptic-bounded generation method is used to simplify the object boundary, especially concave obstacles definition in NMPC constraints, while Extended State Observer is used for observing, compensating the uncertainty terms, and estimating the velocities of the ballbot. In general, by combining this CBF-based NMPC and Quadratic Programming, this research addresses simultaneously high-quality observer, tracking control, balancing control, complex motion planning and safe-angle constraints for the 3D-ballbot system. The effectiveness of our proposed method is determined by simulations in complicated tracking scenarios with static, dynamic and complex-shaped objects.

The Gough-Stewart Platform, often referred to simply as the Stewart Platform, is a parallel mechanical system with six degrees of freedom, which is widely employed in simulation and precise applications. This study gives a thorough Lagrangian-based model of the Stewart Platform, emphasizing its dynamic behavior and control mechanisms. A novel distributed control technique based on Finite-time Distributed Sliding Mode Control (DSMC) is presented to establish second-order consensus in a multi-agent framework in which each leg of the platform is viewed as an autonomous agent. The control approach ensures accurate monitoring of reference trajectories. Simulations are used to validate the efficacy of the proposed control scheme by comparing it to typical decentralized PD control methods. The results simulated based on the Quasi-Physical Model show that consensus-based control outperforms the counterpart control approaches in terms of accuracy and stability.

This paper introduces a comprehensive motion planning–tracking–safety constraint scheme for a 3D ballbot system. A nonlinear control for the 3D ballbot system is designed based on three separate planes by utilizing extended state observer (ESO) to estimate coupling mechanisms. Three virtual control signals are generated from these distinct planes and can be used for formulating actual control signals. To overcome the complexity of nonlinear motion equations, flatness theory is used to construct the time-optimal trajectory through an optimization problem, facilitating smooth movement of the ballbot, and obstacle avoidance based on RRT* waypoints. Furthermore, our work manipulates the hierarchical sliding mode controller (HSMC) as the nominal controller to ensure that the ballbot tracks to the optimal trajectory, unifying with the exponential control barrier function (ECBF) to address safety constraints in the body's deflection angle. Through extensive simulations and comparative analysis, the system demonstrates its effectiveness and safe operation in various working conditions.