Maximum DLCC of Spatial Cable Robot for a Predefined Trajectory Within the Workspace Using Closed Loop Optimal Control Approach

One of the most important applications of cable robots is load carrying along a specific path. Control procedure of cable robots is more challenging compared to linkage robots since cables can’t afford pressure. Meanwhile carrying the heaviest possible payload for this kind of robots is desired. In this paper a nonlinear optimal control is proposed in order to control the end-effector within a predefined trajectory while the highest Dynamic Load Carrying Capacity (DLCC) can be carried. This purpose is met by applying optimum torque distribution among the motors with acceptable tracking accuracy. Besides, other algorithms are applied to make sure that the allowable workspace constraint is also satisfied. Since the dynamics of the robot is nonlinear, feedback linearization approach is employed in order to control the end-effector on its desirable path in a closed loop way while Linear Quadratic Regulator (LOR) method is used in order to optimize its controlling gains since the state space is linearized by the feedback linearization. The proposed algorithm is supported by doing some simulation studies on a two Degrees of Freedom (DOF) constrained planar cable robot as well as a six DOFs under constrained cable suspended robot and their DLCCs are calculated by satisfying the motor torque, tracking error and allowable workspace constraints. The results including the angular velocity, motors’ torque, actual tracking of the end-effector and the DLCC of the robot are calculated and verified using experimental tests done on the cable robot. Comparison of the results of open loop simulation results, closed loop simulation results and experimental tests, shows that the results are improved by applying the proposed algorithm. This is the result of tuning the motors’ torque and accuracy in a way that the highest DLCC can be achieved.     

Optimal regulation of a cable suspended robot equipped with cable interfering avoidance controller

Closed-loop regulation of a spatial cable suspended robot is performed in this paper subject to maximizing the Dynamic Load Carrying Capacity (DLCC) of the end-effector while the cable interference is avoided actively. Optimization is performed between two predefined boundaries and considering the cable interference constraint. This constraint is satisfied by designing a controller which prevents the cables’ collision. The overall formulation of the closed-loop optimal control based on Feedback linearization is derived in this paper for planning the optimal path with the highest load capacity. Then a complementary adaptive controller is designed and implemented to the main controller which is responsible for providing cable interfering avoidance. The efficiency of the designed controller for preventing the cables’ collision is shown by performing and analyzing some comparative simulations conducted on an under constrained cable robot with six cables and six DOFs. All results related to regulation, tracking and DLCC are compared between the simple optimal closed-loop system and the system which is equipped with the proposed cable interfering avoidance controller. It is proved that the planned path satisfies cable interference constraint while its DLCCs are optimized.     

Decoupling and tracking control for elastic joint robots with coupled joint structure

The paper deals with the modeling, identification, and control of a flexible joint robot developed for medical applications at the German Aerospace Center (DLR). In order to design anthropomorphic kinematics, the robot uses a coupled joint structure realized by a differential gearbox, which however leads to strong mechanical couplings inside the coupled joints and must be taken into account. Therefore, a regulation MIMO state feedback controller based on modal analysis is developed for each coupled joint pair, which consists of full state feedback (motor position, link side torque, as well as their derivatives). Furthermore, in order to improve position accuracy and simultaneously keep good dynamic behavior of the MIMO state feedback controller, a cascaded tracking control scheme is proposed, based on the MIMO state feedback controller with additional feedforward terms (desired motor velocity, desired motor acceleration, derivative of the desired torque), which are computed in a computed torque controller and take the whole rigid body dynamics into account. Stability analysis is shown for the complete controlled robot. Finally, experimental results with the DLR medical robot are presented to validate the practical efficiency of the approaches.     

The design and control of a robot finger for tactile sensing

This article describes the design and control of a lightweight robot finger intended for tactile sensing research. The finger is a three-link planar chain with the joints actuated through cables by two motors. Kinematic coupling of the three joints provides two degrees of freedom for finger tip manipulation, and a curling action of the finger for enclosing an object. Hall effect sensors in each joint provide position feedback, and strain gage sensors on each cable provide tension information. To minimize weight and power consumption, a high speed low torque motor together with a 172:1 speed reducer is used as the actuator. A force control loop around the motor speed reducer system reduces the effect of the friction inherent in the speed reducer. Flat mounting plates are provided on each link for special purpose grasping surfaces and sensors.     

Development of flexible joints for a humanoid robot that walks on an oscillating plane

In this study, we develop flexible joints for a humanoid robot that walks on an oscillating plane and discuss their effectiveness in compensating disturbances. Conventional robots have a rigid frame and are composed of rigid joints driven by geared motors. Therefore, disturbances, which may be caused by external forces from other robots, obstacles, vibration and oscillation of the surface upon which the robot is walking, and so on, are transmitted directly to the robot body, causing the robot to fall. To address this problem, we focus on a flexible mechanism. We develop flexible joints and incorporate them in the waist of a humanoid robot; the experimental task of the robot is to walk on a horizontally oscillating plane until it reaches the desired position. The robot with the proposed flexible joints, reached the goal position despite the fact that the controller was the same as that used for a conventional robot walking on a static plane. From these results, we conclude that our proposed mechanism is effective for humanoid robots that walk on an oscillating plane.     

A new approach to robust position/force control of flexible-joint robot manipulators

In this paper a new approach employing smooth robust compensators is proposed for the control of uncertain elastic-joint robot manipulators during contact tasks. It is assumed that the flexible-joint manipulators consist of two subsystems: the rigid subsystem and the flexible subsystem. The output of the flexible subsystem is assumed to be the input of the rigid subsystem. The control design is carried out in two steps. First, a desired input is designed for the rigid subsystem, which can robustly stabilize it. Second, a robust controller is designed to stabilize the flexible subsystem so that it generates the necessary torque designed for the rigid subsystem. By using this approach, the robot manipulator can exert a preset amount of force on the environment while tracking a desired trajectory with global asymptotic stability. Lyapunov's direct method is used here to prove the global asymptotic stability of the closed-loop system. The assumption of weak joint elasticity is relaxed and exact knowledge of joint stiffness is not required for the control design. Also, exact knowledge of robot kinematic and dynamic parameters and actuator parameters are not required. Unlike other approaches, this approach takes the environmental stick-slip friction as well as its dependency on normal contact force into consideration. It compensates for the adverse effects of the stick-slip friction. The proposed controller produces a smooth control action, and ensures smooth motion on the contact surface. The efficacy of the proposed controller is illustrated with the help of a numerical example of a two-link flexible-joint robot. © 1996 John Wiley & Sons, Inc.     

Preshaping input trajectories of industrial robots for vibration suppression

This paper presents several novel methods that improve the current input shaping techniques for vibration suppression for multi-degree of freedom industrial robots. Three different techniques, namely, the optimal S-curve trajectory, the robust zero-vibration shaper, and the dynamic zero-vibration shaper, are proposed. These methods can suppress multiple vibration modes of a flexible joint robot under a computed torque control based on a rigid model. The time delays for each method are quantified and compared. The optimal S-curve trajectory finds the maximum jerk to obtain the minimum vibration. The robust zero-vibration shaper can suppress multiple modes without an accurate model. The delay of the dynamic zero-vibration shaper is smaller than the existing input shaping techniques. Our analysis is verified both by simulation and experiment with a six degrees-of-freedom commercial industrial robot.     

位－力驱动的线驱连续型机器人的动力学建模及实验验证

提出了一种位－力混合驱动的线驱连续型机器人的动力学模型。首先,基于集中质量矩阵法进行机器人动力学建模,将机器人动能的连续积分等效离散为三点求和形式,可简化建模过程并提升仿真的计算效率。其次,分析了驱动力与驱动线几何约束的力学关系,将线驱动作用等效建模为电机的驱动参数与牵引线张力的线性方程组,不仅可以精确地满足牵引线对系统的约束条件,还可以在不使用拉力传感器的条件下得到线的驱动力,降低了机器人成本及控制难度,这种方法适用于任意数量牵引线的连续型机器人。最后,将线驱连续型机器人的仿真和实验结果进行对比,机器人末端点的轨迹最大误差为3.85%,验证了所提模型的有效性。     

Joint acceleration feedback control for robots: analysis, sensing and experiments

Independent joint control for robots is enhanced to suppress the dynamic couplings by incorporating an acceleration feedback loop that is designed in terms of its stability and ability in resisting the dynamic coupling disturbances. The sensing and modeling of joint acceleration via linear accelerometers is dealt from the viewpoint of practical implementation. Extensive experiments are conducted on a three-link direct drive robot, to mainly investigate the ability of the independent joint controller with the acceleration loop in resisting the coupling torque, and demonstrating the enhanced trajectory tracking performance. Results are given against the ones obtained by conventional independent joint control without the acceleration feedback control.     

Robust dynamic surface control of flexible joint robots using recurrent neural networks

A robust neuro-adaptive controller for uncertain flexible joint robots is presented. This control scheme integrates H-infinity disturbance attenuation design and recurrent neural network adaptive control technique into the dynamic surface control framework. Two recurrent neural networks are used to adaptively learn the uncertain functions in a flexible joint robot. Then, the effects of approximation error and filter error on the tracking performance are attenuated to a prescribed level by the embedded H-infinity controller, so that the desired H-infinity tracking performance can be achieved. Finally, simulation results verify the effectiveness of the proposed control scheme.     

On tracking control of flexible robot arms

A controller for solving the tracking problem of flexible robot arms is presented. In order to achieve this goal, the desired trajectory for the link (flexible) coordinates is computed from the dynamic model of the robot arm and is guaranteed to be bounded, and the desired trajectory for the joint (rigid) coordinates can be assigned arbitrarily. The case of no internal damping is also considered, and a robust control technique is used to enhance the damping of the system     

带执行器饱和的柔性关节机器人位置反馈动态面控制

针对带有执行器饱和的柔性关节机器人系统,提出一种位置反馈动态面控制,以实现机器人连杆的角位置跟踪.在一般动态面控制的设计框架下,设计观测器重构系统未知速度状态,利用径向基函数神经网络学习饱和非线性特性,结合“最小参数学习”算法减轻计算负担.通过Lyapunov方法证明得出闭环系统所有信号半全局一致有界,跟踪误差可以通过调节控制器参数达到任意小.仿真结果表明,控制系统能够克服外界干扰,有效补偿系统存在的执行器饱和,实现柔性关节机器人的准确跟踪控制.该方法避免了传统反演设计存在的“微分爆炸”现象,简化了设计过程.     

Reducing flexible base vibrations through local redundancy resolution

Future space systems will use teleoperated robotic systems mounted on flexible bases such as the Shuttle Remote Manipulator System. Due to dynamic coupling, a major control issue associated with these systems is the effect of flexible base vibrations on the performance of the robot. If uncompensated, flexible vibrations can lead to inertial tracking errors and an overall degradation in system performance. One way to overcome this problem is to use kinematically redundant robots. Thus, this article presents research results obtained from locally resolving kinematic redundancies to reduce or damp flexible vibrations. Using a planar, three-link rigid robot example, numerical simulations were performed to evaluate the feasibility of three vibration damping redundancy control algorithms. Results showed that compared to a zero redundancy baseline, the three controllers were able to reduce base vibration by as much as 90% in addition to decreasing the required amount of joint torque. However, similar to locally optimizing joint torques, excessive joint velocities often occurred. To improve stability, fixed weight, multi-criteria optimizations were performed. © 1995 John Wiley & Sons, Inc.     

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided.      

On the Passivity-Based Impedance Control of Flexible Joint Robots

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.     

Cooperative Control of a 3D Dual-Flexible-Arm Robot

This paper discusses cooperative control of a dual-flexible-arm robot to handle a rigid object in three-dimensional space. The proposed control scheme integrates hybrid position/force control and vibration suppression control. To derive the control scheme, kinematics and dynamics of the robot when it forms a closed kinematic chain is discussed. Kinematics is described using workspace force, velocity and position vectors, and hybrid position/force control is extended from that on dual-rigid-arm robots. Dynamics is derived from constraint conditions and the lumped-mass-spring model of the flexible robots and an object. The vibration suppression control is calculated from the deflections of the flexible links and the dynamics. Experiments on cooperative control are performed. The absolute positions/orientations and internal forces/moments are controlled using the robot, each arm of which has two flexible links, seven joints and a force/torque sensor. The results illustrate that the robot handled the rigid object damping links' vibration successfully in three-dimensional space.     

An instrumental variable approach for rigid industrial robots identification

This paper deals with the important topic of rigid industrial robots identification. The usual identification method is based on the use of the inverse dynamic model and the least-squares technique. In order to obtain good results, a well-tuned derivative bandpass filtering of joint positions is needed to calculate the joint velocities and accelerations. However, we can doubt whether the bandpass filter is well-tuned or not. Another approach is the instrumental variable (IV) method which is robust to data filtering and which is statistically optimal. In this paper, an IV approach relevant for identification of rigid industrial robots is introduced. The set of instruments is the inverse dynamic model built from simulated data which are calculated from the simulation of the direct dynamic model. The simulation assumes the same reference trajectories and the same control structure for both the actual and the simulated robot and is based on the previous IV estimates. Furthermore, to obtain a rapid convergence, the gains of the simulated controller are updated according to IV estimates. Thus, the proposed approach validates the inverse and direct dynamic models simultaneously and is not sensitive to initial conditions. The experimental results obtained with a 2 degrees of freedom (DOF) planar prototype and with a 6 DOF industrial robot show the effectiveness of our approach: it is possible to identify 60 parameters in 3 iterations and in 11 s.     

基于干扰观测器的机器人关节控制

提出了基于干扰观测器的仿人机器人关节控制方法。在建立仿人机器人单关节物理模型的基础上,设计了相应的干扰观测器和控制器,解决了关节控制中时变非线性的重力力矩对控制性能的影响。与PID控制器进行性能比较,并探讨了关节模型摄动对干扰观测器的影响,仿真结果表明该方法在仿人机器人关节控制中的可行性和有效性。     

Global output-feedback tracking and load disturbance rejection for electrically-driven robotic manipulators with uncertain dynamics

In this paper the tracking problem for rigid robot manipulators with uncertain parameters and unmodelled torque actuators (DC motors) is addressed and solved by combined first/second-order sliding mode control methodology. The robot is electrically-driven through a pulse-width modulated actuator supply voltage. The proposed controller does not require the availability of the joint velocity, is insensitive to smooth load disturbances and guarantees a global domain of attraction. Computer simulations confirm the feasibility of the proposed approach.     

Generation of feasible set points and control of a cable robot

Cable-suspended robots are structurally similar to parallel-actuated robots, but with the fundamental difference that cables can only pull the end-effector, but not push it. These input constraints make feedback control of cable-suspended robots a lot more challenging than their counterpart parallel-actuated robots. In this paper, we present a computationally efficient control design procedure for a cable robot with six cables, which is kinematically determined as long as all cables are in tension. The control strategy is based on dynamic aspects of statically feasible workspace. The basic idea suggested in this paper is to represent the reachable domain in terms of achievable set points under a specified control law that respects the input constraints. This computational framework is recursively used to find a set of reachable domains, using which, we are able to expand the region of feasibility by connecting adjacent domains through common points. The salient feature of the technique is that it is computationally efficient, or online implementable, for the control of a cable robot with positive input constraints. However, due to the complexity of the dynamics of general motion of a cable robot, we consider only translations. No cable interference is considered in this paper. Finally, the effectiveness of the proposed method is illustrated by numerical simulations and laboratory experiments on a six-degree-of-freedom cable-suspended robot.