Constrained Optimal Control of Cable-Driven Parallel Robots Based on SDRE

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.

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.

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.

Cable-driven parallel robots (CDPRs) are a new type of parallel robots that use cables to control a mobile platform. They possess several advantages, including large workspace, low inertia, and high payload capacity. However, there are several problems in the high-precision trajectory tracking control of CDPRs. On the one hand, all the cables must remain in tension during the entire motion process. On the other hand, the controller design is subjected to model uncertainties and external disturbances. Accordingly, this article proposes a robust synchronization control (RSC) scheme in the cable length space to achieve high-precision trajectory tracking. The synchronization control ensures motion coordination among all the cables and prevents cable relaxation, whereas the robust control eliminates modeling errors and restrains external disturbances. The uniformly ultimate boundedness of the tracking and synchronization errors in the closed-loop system equation was proved using the Lyapunov theory. Simulations and experiments of the trajectory tracking control were both implemented on a three-degree-of-freedom CDPR. Compared with the adaptive robust control scheme and the augmented proportional derivative scheme on the premise of the approximate energy consumption, the proposed RSC scheme could reduce not only the tracking errors of the cables but also the synchronization errors between adjacent cables. Moreover, the RSC scheme could significantly improve the trajectory tracking accuracy of the mobile platform. The robustness of this scheme was verified using load experiments and torque-disturbance experiments.

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.

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.

Although workspace is essential for the design and control of cable-driven parallel robots very few works have been devoted to this topic when sagging cables are considered, most probably because of the complexity of the cable model. In this paper we consider a CDPR with 6 sagging cables whose lengths have a limited maximal value. We propose an algorithm to compute the border of horizontal cross-section of the workspace for a given altitude and orientation of the platform. We show that the singularity of the inverse kinematics equations have to be taken into account for a proper determination of the border.

Adaptive control of parallel robots with uncertain kinematics and dynamics

The research explores the design and fabrication of a cable-driven parallel robot (CDPR) as an innovative and alternative method for in-situ robotic construction. CDPRs consist of a mobile platform attached to a fixed frame by several cables that are controlled through actuating winches. Their increased mobility reveals an immense potential for in-situ design-fabrication solutions emphasizing the importance of local materials and local economies. The paper presents a facet of this research focusing on the development of a novel design tool for the control and simulation of cable-suspended parallel robots in order to facilitate architectural design-fabrication explorations while addressing the complexities associated with parallel robots.

The main concern of this paper is modeling and control of a cable-suspended parallel robot. Alongside lots of benefits, a major open issue in the design of these robots is ensuring tensile cable forces for any admissible motion. The latter problem is particularly challenging when under-constrained configurations are considered. In this paper kinematics, statics and dynamics model of the cable-suspended parallel robot is introduced in a general form. Towards ensuring positive and bounded cable tensions in under-constrained robot Fmincon function of Matlab is used. The proposed method, uses cables tension limits and Jacobian matrix. The controller take benefits from computed torque method which is powerful method for dynamic models. The method is explained and the results achieved prove that the proposed method may a priori ensure positive and bounded cable tensions along desired path.

(also presented ar ICRA'19)

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The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

This paper focuses on various control strategies for a modular cable-articulated parallel robotic manipulator called PACER (Parallel Articulated-Cable Exercise Robot). The proposed robotic device is comprised of multiple cables and a single antagonistically actuated prismatic joint which connects a six degrees-of-freedom moving platform to a fixed base. This novel design provides an attractive architecture for implementation of a home-based rehabilitation device as an alternative to expensive serial robots. In this paper, after deriving the dynamic equations via Newton-Euler formulation, the development of different control strategies in the context of upper limb rehabilitation in three-dimensional space will be examined. The various control modes include: (i) passive mode through feedback linearization for recovering functionalities of the joints at the first step of post-stroke rehabilitation, (ii) active mode via admittance controller for assisting patient to do tasks better, and finally (iii) resistive mode via stiffness controller for increasing the muscle strength. This is now evaluated via a simulation case-study and development of a physical testbed is underway. Since the human arm consists of seven degrees-of-freedom, and daily activities of upper limbs are combination of motions of these simple joints, this proposed design with various control strategies has enormous potential for neurological remapping and brain plasticity in post-stroke patients with upper limb injuries.

In this paper, a new adaptive tracking controller with learning ability is proposed for fully-constrained cable-driven parallel robots (CDPRs). For these systems, the necessity of maintaining positive and bounded tensions in all cables while coping with disturbances represents a critical control requirement. To achieve this goal, we propose a control law based on adaptive dynamic programming (ADP), with an actorcritic structure. In the critic part, an artificial neural network (NN) approximates the value function which is to evaluate the system performance; in the action part, the controller’s parameters are tuned online to achieve optimal control performance. Additionally, the anti-windup (AW) technique is combined with the adaptive controller to cope with the input saturation problem. The stability of the closed-loop system with the proposed control algorithm is proved using the Lyapunov method. Numerical simulations show the effectiveness of the proposed controller.