Comparison of Extended Jacobian and Lagrange Multiplier Based Methods for Resolving Kinematic Redundancy

Several methods have been proposed in the past for resolving the control of kinematically redundant manipulators by optimizing a secondary criterion. The extended Jacobian method constrains the gradient of this criterion to be in the null space of the Jacobian matrix, while the Lagrange multiplier method represents the gradient as being in the row space. In this paper, a numerically efficient form of the Lagrange multiplier method is presented and is compared analytically, computationally, and operationally to the extended Jacobian method. This paper also presents an improved method for tracking algorithmic singularities over previous work.     

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.     

Calculation of repeatable control strategies for kinematically redundant manipulators

A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end-effector paths. This paper compares two methods for choosing repeatable control strategies which minimize their distance from a nonrepeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse while the second method minimizes the distance of the null vectors associated with the desired and the repeatable inverses. It is then shown how the two techniques can be combined in order to obtain the advantages of both methods. As an illustrative example the pseudoinverse is approximated in a region of the joint space for a seven-degree-of-freedom manipulator.     

Smooth continuous transition between tasks on a kinematic control level: Obstacle avoidance as a control problem

Kinematically redundant robots allow simultaneous execution of several tasks with different priorities. Beside the main task, obstacle avoidance is one commonly used subtask. The ability to avoid obstacles is especially important when the robot is working in a human environment. In this paper, we propose a novel control method for kinematically redundant robots, where we focus on a smooth, continuous transition between different tasks. The method is based on a new and very simple null-space formulation. Sufficient conditions for the tasks design are given using the Lyapunov-based stability discussion. The effectiveness of the proposed control method is demonstrated by simulation and on a real robot. Pros and cons of the proposed method and the comparison with other control methods are also discussed.     

空间机器人捕获非合作目标后的消旋策略及阻抗控制

针对空间机器人捕获自旋目标卫星后的消旋与稳定操作提出了一种阻抗控制方法．首先,基于正序链和逆序链方法推导出空间机器人系统在操作空间中的动力学方程．然后,基于归一化时间设计了目标卫星的快速消旋策略,最优消旋时间由末端执行器的约束条件决定．最后,基于所推导操作空间下的动力学方程,提出了一种消除目标旋转运动并同时稳定基座的阻抗控制方法．在利用7自由度冗余机械臂消除自旋卫星并稳定其基座的案例中给出了仿真结果,验证了所提方法的性能及有效性．     

Position control of two-arm manipulators for coordinated point-to-point motion

A trajectory planning and motion control algorithm is; presented for the point-to-point (PTP) motion of two-arm manipulators cooperating on a task. The proposed method considers the multi-arm manipulator as a system when formulating its kinematic model and obtains a global solution to the system, as opposed to individual arm solutions. For PTP motion control between two arm configurations, a simple trajectory is first assumed by defining joint velocity profiles and maximum allowable task space errors between the two end effectors of the manipulator. The task space errors during the motion are then continuously monitored to take corrective action when necessary to prevent those errors from exceeding the given tolerance limits. The main objective of this method is to reduce the number of inverse kinematics solutions during the real-time control of the two-arm system. The algorithm is illustrated by a numerical example for an eight degree-of-freedom kinematically redundant planar two-arm system.     

Torque distribution using a weighted pseudoinverse in a redundantly actuated mechanism

When mobility, the number of independent variables to describe system motion exactly, is greater than the degree-of-freedom of task space, the system is called a kinematically redundant system. On the other hand, redundant actuation indicates a situation when there are more actuators than a system's mobility. Redundant actuation yields many advantages. First, actuation redundancy can increase the force, velocity and acceleration of an end-effector. Second, if some actuators are out of order, the system can still work well. This fault-tolerant capability is useful for remote control robots in space or nuclear plants. Impulsive force can decrease when modulating arbitrary stiffness without feedback control. The performance of a system can be improved by optimizing redundancy. However, there are some issues of economic efficiency and minimization of a system, because redundant actuation may involve more actuators than non-redundant actuation. In addition, there are infinite torque sets of motors for the same task. We used a weighted pseudoinverse matrix for torque distribution. To reduce the maximum torque, we suggested the use of the minimum norm torque as the weighting values. This method allows for smaller motor capacity, and can contribute to economic efficiency and minimization of a system.     

Obstacle avoidance for kinematically redundant manipulators using a dual neural network.

One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.     

Model-based control of redundantly actuated parallel manipulators in redundant coordinates

Model-based control of parallel kinematics machines (PKM) relies on computationally efficient formulations in terms of a set of independent joint coordinates. Since PKM models are commonly expressed in terms of actuator or end-effector coordinates the models are not valid at input- or output-singularities, respectively. Moreover input-singularities limit the motion range of PKM. Actuation redundancy is a means to increase the singularity-free range of motion. However, due to the redundancy only a subset of the actuator coordinates constitute independent coordinates. This subset corresponds to the actuator coordinates of the non-redundant PKM, which does generally not constitute proper minimal coordinates for the entire workspace. Hence a redundantly actuated PKM (RA-PKM) controlled by a model-based controller in terms of minimal coordinates would exhibit the same limitations as the non-redundant PKM. One approach to tackle this problem is to switch between different minimal coordinates, i.e., different motion equations are used within the controller.In this contribution a computed torque and augmented PD control scheme in redundant coordinates is proposed, as an alternative to coordinate switching, and applied to the control of redundantly actuated PKM. That is, no minimal coordinates are selected. This novel formulation is numerically robust and does not suffer from input- or output-singularities. Even more the formulation is always valid except at configuration space singularities. For the redundancy resolution within the inverse dynamics the pseudoinverse of a rank deficient matrix is required, for which an explicit formulation is presented. For both controllers exponential trajectory tracking is shown. Experimental results are reported for a planar 2 DOF RA-PKM.     

Whole-body impedance control of wheeled mobile manipulators

Humanoid service robots in domestic environments have to interact with humans and their surroundings in a safe and reliable way. One way to manage that is to equip the robotic systems with force-torque sensors to realize a physically compliant whole-body behavior via impedance control. To provide mobility, such robots often have wheeled platforms. The main advantage is that no balancing effort has to be made compared to legged humanoids. However, the nonholonomy of most wheeled systems prohibits the direct implementation of impedance control due to kinematic rolling constraints that must be taken into account in modeling and control. In this paper we design a whole-body impedance controller for such a robot, which employs an admittance interface to the kinematically controlled mobile platform. The upper body impedance control law, the platform admittance interface, and the compensation of dynamic couplings between both subsystems yield a passive closed loop. The convergence of the state to an invariant set is shown. To prove asymptotic stability in the case of redundancy, priority-based approaches can be employed. In principle, the presented approach is the extension of the well-known and established impedance controller to mobile robots. Experimental validations are performed on the humanoid robot Rollin’ Justin. The method is suitable for compliant manipulation tasks with low-dimensional planning in the task space.     

Extended impedance control using real and virtual sensors for redundant manipulators

Control of a redundant manipulator based on an impedance-control framework with multiple simultaneous control sources is described. Each control source provides a different behavior type. An application is decomposed into multiple simultaneous behaviors whose resultant behavior will provide the motion necessary to execute the task. The simultaneous control inputs are merged using impedance control to compute a resultant command to the manipulator. The task space of each behavior can have the dimensionality of the mechanism being controlled. Control of a seven-degree-of-freedom manipulator is described here with an available task space for each behavior of dimensionality seven.     

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.     

Joint trajectory generation for redundant robots in an environment with obstacles

Collision avoidance is an absolutely essential requirement for a robot to complete a task in an environment with obstacles. For kinematically redundant robots, collision avoidance can be achieved by making full use of the redundancy. In this article, the problem of determining collision-free joint space trajectories for redundant robots in an environment with multiple obstacles is considered, and the “command generator” approach is employed to generate such trajectories. In this approach, a nondifferentiable distance objective function is defined and is guaranteed to increase wherever possible along the trajectory through a vector in N(J), the null space of Jacobian matrix J. Algorithms that implement this nondifferentiable optimization problem are fully developed. It is shown that the proposed collision-free trajectory generation scheme is efficient and practical. Extensive simulation results of a four-link robot example are presented and analyzed.     

Failure tolerant teleoperation of a kinematically redundant manipulator: an experimental study

Teleoperated robots in harsh environments have a significant likelihood of failures. It has been shown in previous work that a common type of failure such as that of a joint "locking up," when unidentified by the robot controller, can cause considerable performance degradation in the local behavior of the manipulator even for simple point-to-point motion tasks. The effects of a failure become more critical for a system with a human in the loop, where unpredictable behavior of the robotic arm can completely disorient the operator. In this experimental study involving teleoperation of a graphically simulated kinematically redundant manipulator, two control schemes, the pseudoinverse and a proposed failure-tolerant inverse, were randomly presented under both nonfailure and failure scenarios to a group of operators. Based on performance measures derived from the recorded trajectory data and operator ratings of task difficulty, it is seen that the failure-tolerant inverse kinematic control scheme improved the performance of the human/robot system.     

Robot manipulator control for hazardous waste-handling applications

The U.S. Department of Energy has identified robotics as a major technology to be utilized in its program of environmental restoration and waste management, and in particular has targeted robotic handling of hazardous waste to be an essential element in this program. Successful performance of waste-handling operations will require a robot to perform complex tasks involving both accurate positioning of its end effector and compliant contact between the end effector and the environment, and will demand that these tasks be completed in uncertain surroundings. This article focuses on the development of a robot control system capable of meeting the requirements of hazardous-waste-handling applications and presents as a solution an adaptive scheme for controlling the mechanical impedance of kinematically redundant manipulators. The proposed controller is capable of accurate end effector impedance control and effective redundancy utilization, does not require knowledge of the complex robot dynamic model or parameter values for the robot or the environment, and is implemented without calculation of the robot inverse kinematic transformation. Computer simulation results are given for a 4 degree of freedom redundant robot under adaptive impedance control. These results indicate that the proposed controller is capable of successfully performing tasks of importance in robotic waste-handling applications.     

Dynamics and control of a novel 3-DOF parallel manipulator with actuation redundancy

This paper deals with the dynamics and control of a novel 3-degrees-of-freedom （DOF） parallel manipulator with actuation redundancy. According to the kinematics of the redundant manipulator, the inverse dynamic equation is formulated in the task space by using the Lagrangian formalism, and the driving force is optimized by utilizing the minimal 2-norm method. Based on the dynamic model, a synchronized sliding mode control scheme based on contour error is proposed to implement accurate motion tracking control. Additionally, an adaptive method is introduced to approximate the lumped uncertainty of the system and provide a chattering-free control. The simulation results indicate the effectiveness of the proposed approaches and demonstrate the satisfactory tracking performance compared to the conventional controller in the presence of the parameter uncertainties and un-modelled dynamics for the motion control of manipulators.     

Static modeling and control of redundant manipulators

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.     

Compensation of velocity and/or acceleration joint saturation applied to redundant manipulator

The article describes a new method for velocity/acceleration redistribution in order to compensate joint velocity and/or acceleration saturation. The method is designed for redundant manipulators. When some of the joint velocities/accelerations are in saturation other joints compensate for the lack of the velocity and the velocity in the task space remains unchanged. Without the compensation the task space error would appear. Using the compensation method we can achieve maximal velocity/acceleration in the task space while preserving joint velocity/acceleration within limits. The method is also appropriate to compensate a torque saturation. Additionally, we have introduced a condition that shows if the compensation is kinematically and mathematically possible or not.     

Geometric Motion Control for a Kinematically Redundant Robotic Chain: Application to a Holonomic Mobile Manipulator

For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end‐effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end‐effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail. © 2003 Wiley Periodicals, Inc.     

Reaction torque control of redundant free-floating space robot

This paper presents the reaction torque based satellite base reactionless control or base disturbance minimization of a redundant free-floating space robot. This subject is of vital importance in the study of the free-floating space robot because the base disturbance minimization will result in less energy consumption and prolonged control application. The analytical formulation of the reaction torque is derived in this article, and the reaction torque control can achieve reactionless control and satellite base disturbance minimization. Furthermore, we derive the reaction torque based control of the space robot for base disturbance minimization from both the non-strict task priority and strict task priority control strategy. The dynamics singularity in the proposed algorithm is avoided in this paper. Besides, a real time simulation system of the space robot under Linux/real time application interface (RTAI) is developed to verify and test the feasibility and reliability of the method. The experimental results demonstrate the feasibility of online reaction torque control of the redundant free-floating space robot.