High-Precision Trajectory Tracking Control of Cable-Driven Parallel Robots Using Robust Synchronization

We report the control and simulation of a planar cable-driven parallel robot with four cables. The application of the robot is to fully control the lower limb, shank, for gait rehabilitation. The main challenge in control of the cable-driven parallel robot is to avoid negative cable tensions during dynamic motions. For this purpose a redundant robot with capability to exert a general wrench on the target limb with only positive cable tensions for all the poses of the limb near to the trajectory in the gait cycle is used. It is explained that the proposed robot can control both rotational and translational degree of freedom of the shank without slack cable conditions in the gait cycle. Then the dynamic model and control of the robot is proposed with a strategy to choose the forces of cables in order to avoid the negative tension. Examples of simulation are presented to demonstrate the capability of the robot in efficiently tracking the trajectory.

In cable-driven parallel robots (CDPRs), the cables can only apply tensile force. Therefore, the force control signal of cables must always be positive. In this paper, a novel control method is developed to ensure positive tension distribution (PTD) in CDPRs. The proposed control architecture does not require any redundancy resolution consideration. A non-affine representation for the CDPRs dynamics is first given by imposing tension positiveness within an extended dynamic model. With cable tensions as new state variables for the extended model, a robust controller is then designed using conventional methods for affine systems. Simulations are carried out on a six-degree-of-freedom cable robot to verify the effectiveness of the proposed strategy.

To resolve the problem of high-precision trajectory tracking control under interference conditions in a missile’s mid-guidance phase, according to the constructed nominal trajectory, an improved adaptive high-order sliding mode trajectory tracking controller (AHSTC) is proposed. In this method, the open-loop nominal trajectories are established according to the nonlinear programming and Gaussian pseudospectra method. A high-precision trajectory tracking controller is developed by designing a nonlinear sliding mode surface and an adaptive high-order sliding mode approaching law combined with the trajectory tracking nonlinear error model. To verify the effectiveness and superiority of the proposed method, analysis and simulation are carried out through the example of a missile mid-guidance phase tracking control. Compared to the linear quadratic regulator (LQR) and active disturbance rejection controller (ADRC) method, the simulation results show that the proposed AHSTC method shows faster convergence and improved tracking effect. Therefore, the proposed AHSTC method has a good results and engineering application value.

Considering a simplified model of cables is an essential assumption in the design of state-estimator and vibration control of cable-driven parallel robots (CDPRs). Such an assumption however, impacts the effectiveness of controllers and state-estimators in such systems. This article presents a reaction-based stabilizer for nonmodel-based vibration control of CDPRs to address such model dependence. It is proved analytically that by using only three actuators and not involving the cable-connected winches, the proposed stabilizer regulates all undesired vibrations of the platform. It is also shown that the proposed stabilizer needs only the directly measurable position and velocity of its actuators to form its closed-loop control feedback signals. Effectiveness of the proposed system is more significant in CDPRs with considerable nonlinear effects of cables, where such effects are computationally costly to model, such that the performance of real-time controllers and state-estimators are spoiled. To provide a case study, a multibody nonlinear dynamic model of a suspended CDPR equipped-with the proposed stabilizer with zero cable damping effects is developed in SimMechanics/MATLAB, where a fine-tuned proportional-derivative controller is applied on each actuator to suppress all vibrations of the system. In addition, a suspended CDPR with extremely stretchable nonlinear-stiffness elastomer cables is fabricated and tested, where performance of the proposed stabilizer to suppress the high-amplitude nonlinear oscillations of the whole system is demonstrated.

This paper deals with the vision-based control of cable-driven parallel robots. First, a 3D pose visual servoing is proposed, where the end-effector pose is indirectly measured and used for regulation. This method is illustrated and validated on a cable-driven parallel robot prototype. Second, to take into account the dynamics of the platform and using a Cartesian pose and velocity estimator, a vision-based computed torque control is developed and validated in simulation.

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

Achieving high-precision position control while maintaining positive cable tensions is the most challenging issue for the motion control of cable-driven parallel robots, which should be considered significantly. Different from the existing control schemes with online tension distribution that needs real-time computing in each control cycle, a novel dual-loop dynamic control scheme is proposed in this article, where a paralleled dual-loop tracking strategy is introduced to provide a more compatible scheme, which consists of two tracking loops: 1) the tension control loop and 2) the position control loop. In the former loop, the offline tension distribution is adopted to avoid cable hanging loosely and the real-time feasibility of the distribution method is no longer a necessary demand. In the latter loop, due to the complex dynamics characterized by the cable-driven form, the cooperative motion relation among multiple cables and inevitable external disturbances are investigated comprehensively, and the robust synchronization method is included to guarantee the high-precision position control. Afterward, the Lyapunov method is adopted to analyze the strict stability of the whole closed-loop system with both the position and tension control feedback. The experiments indicate that by synthesizing the two control loops, the proposed scheme can dramatically reduce the tracking errors in the trajectory tracking while avoiding the cable relaxation, and particularly, has a satisfactory control effect when the velocity and acceleration of the trajectory have significant oscillations. Additionally, the strong disturbance rejection ability is also validated via robustness experiments.

In this paper, we investigate the trajectory tracking control problem of surface ships subject to unknown parameters, unknown time-varying disturbances, and input saturation. The input saturation is approximated using a Gaussian error function. The compounded uncertain term caused by the unknown parameters and disturbances is transformed into a linear parametric form with a single parameter called virtual parameter. Then, a novel robust adaptive ship trajectory tracking control law is designed using the adaptive vector-backstepping design method, where the adaptive law online provides the estimation of the virtual parameter. Further, a finite-time control scheme is developed injecting a power function vector of the position and velocity errors into the proposed control scheme such that the control performance is improved. Both our control schemes are simple to compute and easy to implement in engineering applications. Theoretical analysis indicates that the designed control laws can force the surface ship to track the desired trajectory while guaranteeing the global uniform ultimate boundedness of all the signals in the closed-loop trajectory tracking control system of surface ships. Simulation results and comparison verify the effectiveness of our novel robust adaptive trajectory tracking control schemes.

Path planning and tracking control are important modules of mobile robots, which have outstanding advantages in improving the flexibility of mobile robots. However, in the existing applications, these two modules are usually processed separately, which makes the obstacle avoidance process of the mobile robot uncontrollable and reduces the adaptability of the application scenario. In order to realize collision-free high-precision trajectory tracking control of mobile robots in dynamic scenes, this paper proposes an adaptive MPC control method based on curvature constraints, which can improve the safety of operation and reduce the chattering caused by unreasonable paths in the process of operation. Firstly, according to the kinematic constraints of general mobile robots, the constraint model of mobile robot path planning is constructed. At the same time, the adaptive parameter adjustment rules are adopted to realize the balance between the calculation efficiency and the control cycle. Finally, a smooth safe path is obtained by re-fitting the planned path and reprocessing the nodes with excessive curvature. Compared with traditional methods, the proposed method has better advantages.

In this article, robust control schemes are presented for time-varying trajectory tracking control of Wheeled Mobile Robots (WMRs) in the presence of disturbance. First, the robust model predictive control (RMPC) is implemented for the kinematic subsystem by solving the modified optimization problem with the fixed starting point. Second, the robust control is extended for the dynamic subsystem by the Backstepping technique and additional observer. This paper shows how to ensure the stability of the closed-loop tracking error system. The performance of the proposed robust control is verified through simulation studies using Casadi tool.KeywordsModel predictive control (MPC)Wheeled mobile robotic systems (WMRs)Output feedback controlTerminal controllerFeasibility

Cable-driven parallel robots (CDPRs) are gaining recognition for their potential due to their lightweight design, large workspace, and high payload capacity. However, their effectiveness in dynamic and unstructured environments requires more than simple position control; they must also be compliant for safe interaction and have the ability to perform a variety of tasks. This paper introduces a novel, practical, and cost-effective variable stiffness actuator (VSA) for CDPRs, based on a planar involute spring design. The VSA, equipped with dual magnetic encoders for precise deflection measurement and stiffness control, is intended for in-line integration with CDPR cables. This design facilitates seamless transitions between high-stiffness precision tasks and low-stiffness compliant interactions.

Uncertainties are prevalent in real-world applications of bipedal walking robots, which may deteriorate the robot’s locomotion performance and even cause instability. However, designing controllers to address uncertainties for bipedal robotic walking is challenging mainly due to the high complexity of the hybrid walking dynamics under uncertainties. In this paper, an adaptive robust control strategy is proposed by combining control Lyapunov functions and the construction of multiple Lyapunov functions for provably guaranteeing the stability and trajectory tracking performance of fully actuated bipedal robots in the presence of uncertainties such as modeling errors and unmodeled disturbances. Simulation results on a three-dimensional bipedal robot with nine revolute joints were conducted to illustrate that the proposed adaptive robust control law can ensure stability and satisfactory tracking performance in the presence of parametric modeling uncertainties and unmodeled nonlinearities.

This paper addresses the trajectory tracking problem for an redundantly-actuated omnidirectional mobile manipulator system with uncertainties and disturbances. The proposed algorithm is robust adaptive control strategy and the parameter estimates are tuned online. First, for designing controller, the conservative upper-bounded function of dynamic model of omnidirectional mobile manipulator system is derived based on the dynamic structure properties. Then, a robust adaptive control scheme is presented to ensure trajectory tracking effect of this closed-loop system. The asymptotical stability is verified a Lyapunov method. Finally, simulation examples are given to demonstrate the proposed approach can guarantee the whole system converge to the desired manifold with prescribed performance.

<div class="section abstract"><div class="htmlview paragraph">Trajectory tracking control is a critical component of the autopilot system, essential for achieving high-performance autonomous driving. This paper presents the design of a stable, reliable, accurate, fast, and robust trajectory tracking controller. Specifically, a lateral and longitudinal trajectory tracking controller based on a linear parameter time-varying model predictive control (LPV-MPC) framework is designed. Firstly, a three-degree-of-freedom vehicle dynamics model and a tracking error model are established. Secondly, a multi-objective function and constraints considering tracking accuracy and lateral stability are formulated, and the quadratic programming (QP) method is employed to solve the optimization problem. Finally, PID speed tracking control is introduced in the longitudinal control scheme for comparison with the proposed MPC longitudinal speed control. A step velocity tracking test validates the effectiveness of the MPC speed tracking controller. In the lateral control scheme, double lane change and circumferential tests are designed to assess the comprehensive performance of the controller under medium-low adhesion road conditions. Additionally, the trajectory tracking performance of the proposed MPC controller is evaluated by comparing it with traditional Sliding Mode Control (SMC) and Linear Quadratic Regulator (LQR) trajectory tracking controllers. The simulation results indicate that the maximum heading error of the MPC controller is less than 0.09 rad, the heading error remains within 0.05 rad, and the front wheel angle stabilizes within 7.5 degrees under both operating conditions. Furthermore, the MPC controller ensures tracking accuracy and smoothness without any obvious jitter while minimizing control inputs to achieve optimal control, thereby significantly enhancing the accuracy and stability of the vehicle's trajectory tracking.</div></div>

The robotic airship can be used as an aerostatic platform for many potential applications, for example, communication, hovering payload deliveries, data-gathering for research studies, etc. These applications require a fully autonomous perspective of an airship. One of the important aspects of airship autonomy is trajectory tracking control. An airship has complex and uncertain nonlinear dynamics which pose a major challenge for designing a precise trajectory tracking control. This paper addresses the airship trajectory tracking control problem under model uncertainties and wind disturbance. We propose a lumped model uncertainties and wind disturbance estimation approach based on an unscented Kalman filter. The estimated lumped uncertainty is used by the Sliding Mode Controller (SMC) for ultimate control of airship trajectory tracking. This comprehensive algorithm, Unscented Kalman filter-based Sliding Mode Controller (USMC), is used as a robust adaptive control solution to track the desired trajectory. The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis. Simulation results show that the proposed method efficiently tracks the desired trajectory. The method solves the stability, convergence, and chattering problem of SMC without the bound constraint of model uncertainties and wind disturbance.