Improving local torque optimization techniques for redundant robotic mechanisms

Two techniques that improve existing local torque optimization methods for redundant robotic mechanisms are proposed. The first technique is based on a balancing scheme, which balances a joint torque norm against a norm of joint accelerations. Expressions have been derived utilizing the Lagrangian multipliers method. The other technique is based on a torque optimization method which minimizes torques through accelerations, obtained from the null-space of the Jacobian matrix. These accelerations are balanced against the minimum-norm acceleration component in order to improve the performance. Numerical simulations have been carried out which in most cases illustrate good performance capability from the viewpoint of torque optimization and global stability.     

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.     

A dual neural network for constrained joint torque optimization of kinematically redundant manipulators

A dual neural network is presented for the real-time joint torque optimization of kinematically redundant manipulators, which corresponds to global kinetic energy minimization of robot mechanisms. Compared to other computational strategies on inverse kinematics, the dual network is developed at the acceleration level to resolve redundancy of limited-joint-range manipulators. The dual network has a simple architecture with only one layer of neurons and is proved to be globally exponentially convergent to optimal solutions. The dual neural network is simulated with the PUMA 560 robot arm to demonstrate effectiveness.     

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.     

Relation between global velocity and local torque optimization of redundant manipulators

In this article, the relation between the global optimization of joint velocity and local optimization of joint torque is investigated. The local minimization of the weighted joint torques can be matched to the global optimization of the corresponding weighted joint velocities when the weighted matrices satisfy certain sufficient conditions. A straightforward matching is obtained using the local optimization of the inertia inverse weighted dynamic torque and the global minimization of the kinetic energy. Another easy solution can be found, as will be shown later, if the inertia matrix is a constant and gravity is neglected. Based on that, it can be seen why a Cartesian robot, which has a constant inertia matrix, is always stable. © 1994 John Wiley & Sons, Inc.     

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.     

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.     

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.     

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.     

Two recurrent neural networks for local joint torque optimizationof kinematically redundant manipulators

This paper presents two neural network approaches to real-time joint torque optimization for kinematically redundant manipulators. Two recurrent neural networks are proposed for determining the minimum driving joint torques of redundant manipulators for the eases without and with taking the joint torque limits into consideration, respectively. The first neural network is called the Lagrangian network and the second one is called the primal-dual network. In both neural-network-based computation schemes, while the desired accelerations of the end-effector for a specific task are given to the neural networks as their inputs, the signals of the minimum driving joint torques are generated as their outputs to drive the manipulator arm. Both proposed recurrent neural networks are shown to be capable of generating minimum stable driving joint torques. In addition, the driving joint torques computed by the primal-dual network are shown never exceeding the joint torque limits.     

Different-Level Simultaneous Minimization of Joint-Velocity and Joint-Torque for Redundant Robot Manipulators

In J Robot Syst 13(3):177–185 (1996), Ma proposed an efficient technique to stabilize local torque optimization solution of redundant manipulators, which prevents occurrence of high joint-velocity and guarantees the final joint-velocity to be near zero. To prevent the same problems, a different-level simultaneous minimization scheme is proposed in this paper for robotic redundancy resolution, which combines the minimum two-norm joint-velocity and joint-torque solutions via two weighting factors. Physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are also taken into consideration in such a scheme-formulation. Moreover, the proposed different-level simultaneous minimization scheme is resolved at the joint-acceleration level and reformulated as a general quadratic program (QP). Computer-simulation results based on the PUMA560 robot manipulator performing different types of end-effector path-tracking tasks demonstrate the validity and advantage of the proposed different-level simultaneous minimization scheme. Furthermore, experimental verification conducted on a practical six-link planar robot manipulator substantiates the effectiveness and the physical realizability of the proposed scheme.     

A balancing technique to stabilize local torque optimization solution of redundant manipulators

A technique that stabilizes the existing local torque optimization solutions for redundant manipulators is proposed in this article. The technique is based on a balancing scheme, which balances a solution of joint torque-minimization against a solution of joint velocity-minimization. Introducing the solution of joint velocity-minimization in the approach prevents occurrence of high joint velocities, and thus results in stable optimal arm motions and guarantees the joint velocities at end of motion to be near zero. Computer simulations were executed on a three-link planar rotary manipulator to verify the performance of the proposed local torque optimization technique and to compare its performance with existing ones for various straight line trajectories. © 1996 John Wiley & Sons, Inc.     

Null space damping method for local joint torque optimization of redundant manipulators

In this article, a null space damping method is proposed that solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudoinverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by the results of two computer simulations. In addition, the minimization of electrical power consumption is addressed with respect to the results of this article.     

An efficient technique for finding the desired global optimum of robotic joint displacement

For an industrial robot on a daily operation basis such as pick and place, it is desired to minimize the robotic joint displacements when moving the robot from one location to another. The objective of the optimization here is to simultaneously minimize a robot end effector's positional error and the robotic joint displacements. By modifying the searching algorithm in the existing complex optimization method, this article presents a technique for finding the desired global optimum solution more efficiently. To compare the optimum searching capability between the proposed and existing searching algorithms, a modified Himmelblau's function is used as an objective function. The presented technique is then applied to a spatial three-link robot manipulator for global minimization of the joint displacements. © 1992 John Wiley & Sons, Inc.     

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.     

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.     

Globally Optimal Trajectory Planning for Redundant Manipulators using State Space Augmentation Method

The off-line global trajectory planning for kinematically redundant manipulators is formulated as an optimization problem whose solution is obtained by applying the Pontryagins Maximum Principle. The state space augmentation method is developed to obtain a set of optimal joint trajectories corresponding to a singularity-free Cartesian path which avoids joint limits and conserves joint configuration in cyclic motion. Results of computer simulation conducted on a three-degree-of-freedom planar manipulator are presented and discussed.     

Intelligent control of multi-fingered hands

This paper is concerned with intelligent control for grasping and manipulation of an object by multi-fingered robot hands with rigid or soft hemispheric finger ends that induce rolling contacts with the object. Even in the case of 2D motion like pinching by means of a pair of multi-degrees of freedom robot fingers, there arises an interesting family of Lagrange’s equations of motion with many geometric constraints, which are under-actuated, redundant, and non-holonomic in some sense. Regardless of underactuation of dynamics, it is possible to find a class of sensory feedback signals that realize secure grasp of an object together with control of object orientation. In regard to the secure grasping, a problem of force/torque closure for 2D objects in a dynamic sense plays a crucial role. It is shown that proposed sensory feedback signals satisfying the dynamic force/torque closure can be constructed without knowing object kinematic parameters and location of the mass center. To prove the convergence of motion of the overall fingers–object system under the circumstance of redundancy of joints, new concepts called “stability on a manifold” and “asymptotic stability on a manifold” are introduced. Based on the results found for intelligent control of robotic hands, the last two sections attempt to discuss why human multi-fingered hands can become so dexterous at grasping and object manipulation.     

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.     

The dexterity and singularities of an underactuated robot

Underactuated robots are robotic systems with more joints than actuators. A robot may be underactuated by design as in the case of a hyper‐redundant robot with passive joints or may become underactuated as a result of an actuator failure. In this article, we examine the dexterity of underactuated robots whose passive joints operate in either a locked or free‐swinging mode. The ability to an analyze the dexterity of an underactuated robot has important applications especially for the control of passive joints with brakes and for the fault tolerance analysis of an otherwise fully actuated kinematically redundant robot. The approach applied here is to use kinematics and dynamics‐based formulations of manipulator dexterity. We then characterize passive‐joint singularities, i.e., configurations where full end‐effector control is lost because one or more joints are passive instead of active. Lastly, we introduce a new characterization of joint‐limit singularities, which are configurations where full end‐effector control cannot be achieved because one or more joints are at their joint limits. © 2001 John Wiley & Sons, Inc.