Dynamic Load Carrying Capacity of Flexible Cable Suspended Robot: Robust Feedback Linearization Control Approach

In this paper dynamic load carrying capacity (DLCC) of a cable robot equipped with a closed loop control system based on feedback linearization, is calculated for both rigid and flexible joint systems. This parameter is the most important character of a cable robot since the main application of this kind of robots is their high load carrying capacity. First of all the dynamic equations required for control approach are represented and then the formulation of control approach is driven based on feedback linearization method which is the most suitable control algorithm for nonlinear dynamic systems like robots. This method provides a perfect accuracy and also satisfies the Lyapunov stability since any desired pole placement can be achieved by using suitable gain for controller. Flexible joint cable robot is also analyzed in this paper and its stability is ensured by implementing robust control for the designed control system. DLCC of the robot is calculated considering motor torque constrain and accuracy constrain. Finally a simulation study is done for two samples of rigid cable robot, a planar complete constrained sample with three cables and 2 degrees of freedom and a spatial unconstrained case with six cables and 6 degrees of freedom. Simulation studies continue with the same spatial robot but flexible joint characteristics. Not only the DLCC of the mentioned robots are calculated but also required motors torque and desired angular velocity of the motors are calculated in the closed loop condition for a predefined trajectory. The effectiveness of the designed controller is shown by the aid of simulation results as well as comparison between rigid and flexible systems.     

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.     

Neural Network Solution for Forward Kinematics Problem of Cable Robots

Forward kinematics problem of cable robots is very difficult to solve the same as that of parallel robots and in the contrary to the serial manipulators’. This problem is almost impossible to solve analytically because of the nonlinearity and complexity of the robot’s kinematic equations. Numerical methods are the most common solutions for this problem of the parallel and cable robots. But, convergency of these methods is the drawback of using them. In this paper, neural network approach is used to solve the forward kinematics problem of an exemplary 3D cable robot. This problem is solved in the typical workspace of the robot. The neural network used in this paper is of the MLP type and a back propagation procedure is utilized to train the network. A simulation study is performed and the results show the advantages of this method in enhancement of convergency together with very small modeling errors.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

The leader-follower formation control of nonholonomic mobile robots

In this paper, the leader-waypoint-follower formation is constructed based on relative motion states of nonholonomic mobile robots. Since the robots’ velocities are constrained, we proposed a geometrical waypoint in cone method so that the follower robots move to their desired waypoints effectively. In order to form and maintain the formation of multi-robots, we combine stable tracking control method with receding horizon (RH) tracking control method. The stable tracking control method aims to make the robot’s state errors stable and the RH tracking control method guarantees that the convergence of the state errors tends toward zero efficiently. Based on the methods mentioned above, the mobile robots formation can be maintained in any trajectory such as a straight line, a circle or a sinusoid. The simulation results based on the proposed approaches show each follower robot can move to its waypoint efficiently. To validate the proposed methods, we do the experiments with nonholonomic robots using only limited on-board sensor information.     

Dynamic Modeling and Robust Controller Design of a Two-Stage Parallel Cable Robot

Cable robots have been extensively used for the loading and unloading of cargo in shipping industries. In this paper, we look at a two stage cable robot, i.e., a cable robot with two moving platforms connected in series. The sea condition introduces disturbance into the system. This disturbance is considered while modeling the dynamics of the two stage cable robot. A robust controller is designed which can assure robust tracking of the desired end-effector trajectory in the presence of the disturbance. Simulation results presented show the effectiveness of the controller.     

Translational Planar Cable-Direct-Driven Robots

A planar cable-direct-driven robot (CDDR) architecture is introduced with only translational freedoms. The motivation behind this work is to improve the serious cable interference problem with existing CDDRs and to avoid configurations where negative cable tensions are required to exert general forces on the environment and during dynamic motions. These problems generally arise for rotational CDDR motions. Thus, we propose a class of purely translational CDDRs; of course, these are not general but may only perform tasks where no rotational motion or resistance of moments is required at the end-effector. This article includes kinematics and statics modeling, determination of the statics workspace (the space wherein all possible Cartesian forces may be exerted with only positive cable tensions), plus a dynamics model and simulated control for planar translational CDDRs. Examples are presented to demonstrate simulated control including feedback linearization of the 4-cable CDDR (with two degrees of actuation redundancy) performing a Cartesian task. We introduce an on-line dynamic minimum torque estimation algorithm to ensure all cable tensions remain positive for all motion; otherwise slack cables result from the CDDR dynamics and control is lost.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

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.     

Wrench-feasible workspace generation for cable-driven robots

This paper presents a method for analytically generating the boundaries of the wrench-feasible workspace (WFW) for cable robots. This method uses the available net wrench set, which is the set of all wrenches that a cable robot can apply to its surroundings without violating tension limits in the cables. The geometric properties of this set permit calculation of the boundaries of the WFW for planar, spatial, and point-mass cable robots. Complete analytical expressions for the WFW boundaries are detailed for a planar cable robot and a spatial point-mass cable robot. The analytically determined boundaries are verified by comparison with numerical results. Based on this, several workspace properties are shown for point-mass cable robots. Finally, it is shown how this workspace-generation approach can be used to analytically formulate other workspaces.     

Maximum allowable load of flexible manipulators for given dynamic trajectory

This paper presents the formulation and numerical solution of the dynamic load carrying capacity (DLCC) problem of flexible manipulators. For manipulators under the rigid body assumption, the major limiting factor in determining the maximum allowable load (load mass and load moment of inertia) for a prescribed dynamic trajectory (positions, velocities and accelerations) is the joint actuator capacity. But for a flexible robot, an additional constraint on allowable deformation at the end effector must be imposed because either lighter-weight links or operating at a higher speed could cause unacceptable fluctuations when moving along a trajectory. A Lagrangian assumed mode method was used to model the manipulator and load dynamics, including both joint and deflection motions. The deflection equations are then coupled with robot kinematics to solve for the generalized coordinates. A strategy to determine the DLCC subject to both constraints mentioned above is formulated where the end effector deflection is specified in terms of a series of spherical bounds with a radius equal to the allowable deformation. A general computational procedure for the multiple-link case given arbitrary trajectories is described in detail. Symbolic derivation and simulation by using a PC-based symbolic language MATHEMATICA® was carried out for a two-link planer robot. The results confirmed the necessity of the dual constraints and showed that which constraint is more critical for a given robot and trajectory depends on the required accuracy.     

用奇异模型描述的受限机器人的学习控制

本文了一类受限机器人的迭代学习控制方案，控制器的设计是基于机器人模型的降阶形式。在存在有界未知干扰的情况下，对末端操纵器受线性、无摩擦约束面的受限机器人。本文给出的控制方案保证了机器人系统的完全运动跟踪，同时保证了力跟踪误差有界的，且界的大小是可调节的。     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

A force–impedance controlled industrial robot using an active robotic auxiliary device

A strategy to improve the performance of current commercial industrial robots is presented in this paper. This strategy involves cooperation of two robotic manipulators: the robotic controlled impedance device (RCID) and a commercial industrial robot. The RCID is a small six degrees-of-freedom (DOF) high bandwidth force–impedance controlled parallel manipulator, developed at the School of Engineering of the University of Porto (Portugal). The RCID works attached in series with a position controlled commercial industrial robot. Combination of the two manipulators behaves as a single manipulator having the impedance and force control dynamic performance of the RCID, as well as the workspace and trajectory tracking bandwidth of the industrial robot. Force–impedance control of the RCID, and experimental results on typical tasks that involve end-effector contact with uncertain environments of unknown stiffness are presented.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Nonlinear coupling tracking control for underactuated construction lifting robots with load hoisting/lowering under initial input saturations

Underactuated construction lifting robots, which have been widely concerned by erudite researchers, always contain load hoisting/lowering motion. When the cable length is utilized as a variable, construction lifting robots produce violent load swing, which affects the construction safety undoubtedly and brings great challenges to the development of the controller. Moreover, most existing controllers may not take into account issues, such as initial input saturations and poor ability to suppress load swing, and they may utilize linearization or approximation. Inspired by these phenomena, a nonlinear coupling tracking controller for underactuated construction lifting robots with load hoisting/lowering under initial input saturations is proposed. With reference to expected trajectories to ensure the smooth operation of the construction lifting robot system, the initial input saturations are considered to make the trolley and cable start stably, respectively; a coupling signal, which contains actuated variables and underactuated variables, is constructed to improve the transient control performance of construction lifting robots. Combined with theoretical derivation, simulation, and experimental verification, the proposed controller achieves superior control performance, which ensures the accurate positionings of the system, and suppresses and eliminates the load swing effectively, so as to ensure the safe construction; the proposed controller admits outstanding robustness with respect to the changes of system parameters and the adverse effects of external disturbances. The proposed controller provides a novel antiswing strategy for construction lifting robots with load hoisting/lowering, which possesses excellent practical significance.     

A Case Study of the Collision-Avoidance Problem Based on Bernstein–Bézier Path Tracking for Multiple Robots with Known Constraints

In this paper a case study of a new, cooperative, collision-avoidance method for multiple, nonholonomic robots based on Bernstein–Bézier curves is given. In the presented examples the velocities and accelerations of the mobile robots are constrained and the start and the goal velocity are defined for each robot. This means that the proposed method can be used as a subroutine in a huge path-planning problem in real time, in a way to split the whole path into smaller partial paths. The reference path of each robot, from the start pose to the goal pose, is obtained by minimizing the penalty function, which takes into account the sum of all the path lengths subjected to the distances between the robots, which should be bigger than the minimum distance defined as the safety distance, and subjected to the velocities and accelerations which should be lower than the maximum allowed for each robot. When the reference paths are defined the model-predictive trajectory tracking is used to define the control. The prediction model derived from the linearized tracking-error dynamics is used to predict future system behavior. The control law is derived from a quadratic cost function consisting of the system tracking error and the control effort. The proposed method was tested with a simulation and with a real-time experiment in which four robots were used.     

Path Planning of Free Floating Prismatic-Jointed Manipulators

Reaching a desired position with a specific orientationin space by a robot, mounted on a freely floating base, is an importantpath planning and control problem. Research in this area has mainlyconcentrated on the use of revolute-jointed serial manipulators. It iswell known that the dynamic equations of such manipulators are quitecomplex.In this paper, we propose the use of a 6-link fully prismatic-jointedrobot to achieve a desired position and orientation in space instead of arevolute-jointed robot. The use of pure prismatic-jointed robots forsuch a purpose is counter intuitive. On earth, such a structure is unableto provide a desired orientation to the end-effector. However, it can beshown that in space, arbitrary end-effector orientations are possible.Due to the relative simplicity of kinematics, dynamics and workspace ofprismatic-jointed robots compared to revolute-jointed robots, their useresults in significant computational advantages in path planning andcontrol.Also, in this paper, we adopt an unconventional motion planning methodthat avoids inversion of the Jacobian matrix and results in singularityfree paths for the end-effector. In this method, the joint trajectoriesare considered to be modal sums of basis functions of time. Within this framework, constraints on jointangles and joint rates can be imposed. The results are demonstratedwith an example of a 6-link fully prismatic-jointed robot.