A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

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.     

Kinematic control of redundant robots and the motion optimizabilitymeasure

This paper treats the kinematic control of manipulators with redundant degrees of freedom. We derive an analytical solution for the inverse kinematics that provides a means for accommodating joint velocity constraints in real time. We define the motion optimizability measure and use it to develop an efficient method for the optimization of joint trajectories subject to multiple criteria. An implementation of the method for a 7-dof experimental redundant robot is present.     

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.     

Kinematic control of redundant robot manipulators: A tutorial

In this paper, we present a tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators. Our goal is to lend some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator's Jacobian, those based on the local optimization of objective functions in the null space of the Jacobian, those based on the task space augmentation by additional constraint tasks (with task priority), and those based on the construction of inverse kinematic functions.     

Robust adaptive multi-task tracking control of redundant manipulators with dynamic and kinematic uncertainties and unknown disturbances

In this paper, a novel adaptive multi-priority controller for redundant manipulators is proposed to accomplish the multi-task tracking when kinematic/dynamic uncertainties and unknown disturbances exist. Prioritized redundancy resolution in kinematic level is incorporated into this passivity-based control framework. The kinematic and dynamic parameter adaptations are driven by both tracking error and prediction error. Moreover, the tracking information from both primary and subtasks are all utilized to accelerate the parameter estimation when the tasks are independent, whereas the inevitable tracking error of the subtasks due to algorithmic singularities is properly eliminated in the adaptation laws when the tasks are dependent. Potential ill-conditioned solution of the pseudoinverse is avoided using an improved singularity-robust inverse of the projected Jacobian. Along with the improvement of the multi-task tracking performance, smoothness of the commanded torques is still guaranteed for easy application. Measurements of the noisy joint acceleration and task velocity are avoided. The controller is mathematically derived based on Lyapunov stability analysis. Simulation results of the two cases are presented to verify the effectiveness and superiority of the proposed controller.     

冗余机械臂优化控制新方法

针对五自由度冗余机械臂,提出了一种新的基于伪逆的优化控制方法：利用一个可调权值因子,将最小速度范数方法（加速度层）和最小加速度范数方法进行加权组合,来实现对冗余机械臂的运动控制。该优化方法可以实现关节速度范数和关节加速度范数的同时最小化,而且使得机械臂的关节速度在运动末态时接近零。计算机仿真结果进一步验证了所给出的优化控制方法的可行性和优越性。     

An algorithmic approach to coordinate transformation for robotic manipulators

Coordinate transformation is one of the most important issues in robotic manipulator control. Robot tasks are naturally specified in work space coordinates, usually a Cartesian frame, while control actions are developed on joint coordinates. Effective inverse kinematic solutions are analytical in nature; they exist only for special manipulator geometries and geometric intuition is usually required. Computational inverse kinematic algorithms have recently been proposed; they are based on general closed-loop schemes which perform the mapping of the desired Cartesian trajectory into the corresponding joint trajectory. The aim of this paper is to propose an effective computational scheme to the inverse kinematic problem for manipulators with spherical wrists. First an insight into the formulation of kinematics is given in order to detail the general scheme for this specific class of manipulators. Algorithm convergence is then ensured by means of the Lyapunov direct method. The resulting algorithm is based on the hand position and orientation vectors usually adopted to describe motion in the task space. The analysis of the computational burden is performed by taking the Stanford arm as a reference. Finally a case study is developed via numerical simulations.     

Clamping weighted least-norm method for the manipulator kinematic control with constraints

One of the main challenges for kinematic control of manipulators is how to effectively address various constraints, such as obstacle avoidances. Most constraints can be converted into a virtual joint-limit problem by the general weighted least-norm method reported recently. However, a chattering of weighted factors might occur in the presence of disturbances. In this paper, in order to improve the robustness to disturbances, a clamping term forcing joints away from their limits is added to the solution of inverse kinematics, termed as the clamping weighted least-norm method. It is proved that the joint-limit constraint is always guaranteed. The proposed method is applicable to both non-redundant and redundant manipulators; the accuracy of main task is sacrificed only when there is confliction between main task and joint-limit constraint. Experiments on the seven-degree-of-freedom redundant manipulator illustrate the good performance for avoiding joint limits while tracking a given trajectory.     

Identification and resolution of structural and algorithmic singularity in redundancy control of serial manipulations

A major difficulty that has haunted most researchers in the process of optimal redundancy resolution of robotic manipulators is the instability observed in even very simple numerical simulations. This numerical instability is not related to the structurally singular configurations of the manipulators, and in the literature has been referred to as “algorithmic singularity,” “artificial singularity,” or “unavoidable singularity.” In this work, conditions on both structural and algorithmic singularities are studied based on the Singular Value Decomposition of the Jacobian matrix, and, hence, a singularity-free control algorithm for redundant manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that many well-known methods for optimal redundant manipulation in the literature, including the Extended Jacobian Technique, most of constraint function-based methods, and most of the previously reported methods on global optimization techniques, are all special cases of the formulation provided here. Further, the necessary conditions of the global optimality for this general formulation are derived in explicit form and the source of “algorithmic singularity” is rigorously identified and resolved. © 2995 John Wiley & Sons, Inc.     

Homogeneous weighted motion planning for cooperated manipulator systems under position-torque constrained processing Environment

Real-time motion planning under position and torque constraints is a critical challenge for cooperative manipulator efficiency and safety operation. Real-time motion planning at the velocity level improves computation efficiency, eliminates the complex derivative calculation of the Jacobian matrix, and the velocity planning solution can be used directly for robotic kinematic control. However, little research attention has been attached to handling the position and torque constraints simultaneously at velocity level for cooperative manipulator systems. In this paper, we introduce a novel homogeneous weighted least-norm method (HWLN) for joint velocity redistribution of cooperated manipulators. Within the coupled kinematics-dynamics model of cooperated manipulators, joint position and torque constraints are simultaneously homogenized and taken into account by the constraint performance index. To avoid joint's constraint saturations, two real-time weight updating laws are designed for the joint position and driving torque respectively. The joint velocities of cooperated manipulators are then adaptively redistributed using the pseudo-kinetic-energy minimum optimization criteria. When compared to single manipulator regulation, this strategy takes greater advantage of cooperative redundancy and significantly enhances the position-torque planning performance. Mathematical stability proof is presented. In the meanwhile, numerical experiment results under various joint position and torque constraints demonstrate the effectiveness of the proposed HWLN method. The experimental results for motion planning and control of two 6R ABD-20Kg robotic manipulators are provided.     

Mobile Manipulator Motion Planning for Multiple Tasks Using Global Optimization Approach

A mobile manipulator can perform various tasks efficiently by utilizing mobility and manipulation functions. The coupling of these two functions creates a particular kinematic redundancy introduced by mobility, which is different from that introduced by extra joints. This redundancy is quite desirable for dexterous motion in cluttered environments, but it also significantly complicates the motion planning and control problem. In this paper we propose a new motion planning method for mobile manipulators to execute a multiple task which consists of a sequence of tasks. The task considered in this paper is that the end-effector tracks a prespecified trajectory in a fixed world frame. In a multiple task, the final configuration of each task becomes the initial configuration of the next subsequent task. Such a configuration is known as a commutation configuration, which significantly affects the performance of the multiple task.We formulate the motion planning problem as a global optimization problem and simultaneously obtain the motion trajectory set and commutation configurations. In the formulation, we take account of the case that the platform has a non-holonomic constraint as well as the one that the platform has a holonomic constraint. Simulation results are demonstrated to verify the effectiveness of the proposed method.     

The optimum design of robotic manipulators using dexterity indices

This paper presents new dexterity indices that can be applied to planar and spatial manipulators. These indices are based on the condition number of the Jacobian matrix of the manipulators which is known to be a measure of their kinematic accuracy. Dexterity indices based on that same criterion have been presented elsewhere. However, due to the formulation of the kinematic equations, the existing indices are affected by a scaling of the manipulator when both the position and the orientation of the end effector are included in the kinematic equations. A new formulation of these equations is proposed here to avoid this problem of dimensional dependence. Two dexterity indices are presented for planar manipulators: the first one is based on a redundant formulation of the velocity equations whereas the second one is based on the mininum number of parameters. The corresponding indices are also derived for spatial manipulators. Finally, an example is included to illustrate the use of these indices in the context of design and optimization of manipulators.     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

Reliable computation of minimum-time motions for manipulators moving in obstacle fields using a successive search for minimum-overload trajectories

In this paper we present a practical method for finding obstacle-free minimum-time motions for manipulators subject to the limits of velocity-dependent actuator forces. An optimal motion-planning problem is converted into a finite-dimensional nonlinear programming problem by means of parameter optimization with quintic B-splines. We introduce the concept of the minimum-overload trajectory in which the motion time is specified to be faster than the actuators can handle, and the actuator overloads are minimized with the motion time fixed. By successive searches for minimum-overload trajectories, minimum-time motions are determined for three example manipulators without simplifying any of the kinematic, dynamic or geometric properties of the manipulators or the obstacles. In the resultant minimum-time motions, almost all of the joint actuators are close to saturation during the motions. © 2005 Wiley Periodicals, Inc.     

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator’s locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.     

Null torque-based dynamic control for kinematically redundant manipulators

For the dynamic control of kinematically redundant manipulators, conventional approaches to local torque minimization have induced physically unachievable joint torques that may exceed the torque limits in the tracing motion of a long end-effector trajectory. This article presents a new control method for redundant manipulators, named the “Null Torque-Based Dynamic Control” (NTDC), which can guarantee stability for joint torques. The proposed method resolves the redundancy at the torque level. The command torque induced by the proposed method is composed of two terms: (1) the minimum-norm torque, which locally minimizes torque loadings at the joints; and (2) the null torque, which is intermittently added to the minimum-norm torque according to a kinematic criterion to globally reduce excessively large torque requirements. In particular, the concept of null torque is based on the property of full row-rank minors for a Jacobian matrix—the aspect that is a function of a manipulator's configuration. The simulation results illustrate that the proposed method is effective for torque optimization when compared with conventional methods.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.