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.     

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.     

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.     

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.     

Optimization techniques applied to multiple manipulators for path planning and torque minimization

This paper presents the formulation and application of a strategy for the determination of an optimal trajectory for a multiple robotic configuration. Genetic Algorithm (GA) and Simulated Annealing (SA) have been used as the optimization techniques and results obtained from them compared. First, the motivation for multiple robot control and the current state-of-art in the field of cooperating robots are briefly given. This is followed by a discussion of energy minimization techniques in the context of robotics, and finally, the principles of using genetic algorithms and simulated annealing as an optimization tool are included. The initial and final positions of the end effector are specified. Two cases, one of a single manipulator, and the other of two cooperating manipulators carrying a common payload illustrate the proposed approach. The GA and SA techniques identify the optimal trajectory based on minimum joint torque requirements. The simulations performed for both the cases show that although both the methods converge to the global minimum, the SA converges to solution faster than the GA.     

A new method for actuating parallel manipulators

This paper presents a new technique of actuating a parallel platform manipulator using shape memory alloy (SMA). This is a type of smart materials that can attain a high strength-to-weight ratio, which makes them ideal for miniature application. The work is mainly to develop a new SMA actuator and then incorporating the actuator in building the parallel manipulator prototype. The SMA used in this study is a commercial NiTi wire. The SMA wire provides an actuating force that produces a large bending and end displacement. A 3-UPU (universal–prismatic–universal) parallel manipulator using linear SMA actuators was developed. The manipulator consists of a fixed platform, a moving platform and three SMA actuators. The manipulator workspace was specified based on the restrictions due to actuator strokes and joint angle limits. System identification techniques were used to model both heating and cooling processes. An ON/OFF control was performed and the results showed closeness in simulation and experimental results. This study showed that shape memory alloy actuated beam can successfully be used to provide linear displacement. The built prototype indicates the feasibility of using SMA actuators in parallel manipulators.     

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.     

Different-level two-norm and infinity-norm minimization to remedy joint-torque instability/divergence for redundant robot manipulators

To remedy the joint-torque instability/divergence phenomenon arising in the conventional infinity-norm torque-minimization (INTM) scheme, and prevent the occurrence of high joint-velocity and joint-acceleration as well, a different-level bi-criteria minimization scheme is proposed and investigated in this paper for redundant robot manipulators with physical constraints (e.g., joint-angle limits, joint-velocity limits and joint-acceleration limits) considered. Such a scheme combines the minimum two-norm joint-velocity and infinity-norm joint-torque solutions via a weighting factor, which guarantees the final joint-velocity of the motion to be near zero (more acceptable for engineering application). In addition, the different-level scheme is reformulated as a general quadratic program (QP) and resolved at the joint-acceleration level. Computer-simulation results based on the PUMA560 robot manipulator further demonstrate the effectiveness and advantages of the proposed different-level bi-criteria minimization scheme for robotic redundancy resolution.     

A direct variational method for planning monotonically optimal paths for redundant manipulators in constrained workspaces

This paper proposes a path planner for serial manipulators with a large number of degrees of freedom, working in cluttered workspaces. Based on the variational principles, this approach involves formulating the path planning problem as constrained minimization of a functional representing the total joint movement over the complete path. We use modified boundary conditions at both ends of the trajectory to find more suitable start and end configurations. The concept of monotonic optimality is introduced in order to optimize the manipulator paths between the resulting end configurations. For obstacle avoidance, volume and proximity based penalizing schemes are developed and used. The presented planner uses a global approach to search for feasible paths and at the same time involves no pre-processing task. A variety of test cases have been presented to establish the efficacy of the presented scheme in providing good quality paths. The extent of advantage accruing out of the measures of free end-configurations and monotonic optimality are also analyzed quantitatively.     

A practical method for the deformation of long-stroke hydraulic manipulators in grasping-handling tasks

Long-stroke hydraulic manipulators are utilized in various grasping-handling tasks, and the flexible deformation of these manipulators is the primary obstacle that affects precise position control of the end-effectors in Cartesian space. This deformation is manifested in the following three aspects: joint deformation, structural deformation and clearance variation. Due to deformation uncertainty, methods that model the hydraulic manipulator as a combination of flexible multibody systems and hydraulic actuators are unsuitable. In this article, we propose an incremental inverse kinematics model (IIKM) as a new approach to solving the above deformation difficulties. The projection method is used to obtain the inverse kinematic analytical solution of long-stroke hydraulic manipulators, which is based on the manipulator deformation in the current configuration (current configuration refers to the arrangement of the manipulator links when the manipulator starts to move to the target position). The proposed method avoids complex flexible multibody modeling and parameter identification, allowing long-stroke hydraulic manipulators to be accurately controlled within a certain neighborhood. An evaluation coefficient is proposed to analyze the calculation accuracy of the IIKM in combination with the success rate obtained from 190 grasping experiments. Through these experiments, we determine the optimal calculation height range of the IIKM in the vertical direction and the optimal calculation position area in the horizontal direction and prove that the IIKM result can guarantee the success of grasping-handling tasks when the end-effector is within the optimal calculation height range.     

Novel approaches to control multiple tasks in redundant manipulators: stability analysis and performance evaluation

In this paper, two new approaches for handling multiple tasks in redundant manipulators based on predefined allocated priorities are proposed. The first approach is an integrated scheme which employs null-space base vector for handling prioritized tasks. Clear task and null-space representation, better execution of the lower priority tasks, and intuitive formulation are its basic features. The second approach aims to improve the performance of all the prioritized tasks, especially during algorithmic singularities beside clear null-space dynamics representation. This approach can be considered as a modification and extension of the Reverse Priority (RP) algorithm in acceleration level. The commands related to each tasks are added to each other following reverse order of priorities and by suitable projectors. The projector definition is given using minimal representation of the null-space. Clear null-space dynamics in the proposed methods facilitate the stability analysis. A detailed evaluation by means of computer simulation in various cases is reported. Tasks accomplishment using the proposed approaches is compared with the classic method. The results, in general, show higher performance and accuracy of the tasks by the proposed approaches.     

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.     

A new method for solving kinematic tasks for robots

The main difficulties in solving inverse kinematic tasks for robots are singularities and nonlinearities. In the first part of this paper practical conditions regarding singularities of 6 df wrist-joint structure robots are presented. These considerations are based on a simple iterative inversion method by the use of which introduction and characterization of the concepts of “essential” and “procedural” singularities are realized. The second part of the paper deals with the question of nonlinearities. It is pointed out that in robotics there are two different kinds of nonlinearities. The first type is present because the sine and cosine functions of the joint coordinates appear in the formulae of direct kinematic tasks. The second type is of finite polynomial nature, and originates from the quadratic functions of the unit vectors parallel to the rotation axes of the joints of the arm. The authors point out that an appropriate quaternion representation of the robot kinematics offers a convenient possibility to get rid of sine- and cosine-type nonlinearities. Those nonlinearities which remain are the results of simple quadratic operations (mainly multiplications and additions, subtractions and divisions); therefore the proposed method seems to be especially appropriate for realizations based on neural networks or particular hardwares using RISC processors. The advantages and disadvantages of this new method are compared to those of another solution recently published by the authors.     

Analytic minimum-norm solution for rate coordination in redundant manipulators

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.     

An improved trajectory planner for redundant manipulators in constrained workspace

This article studies the trajectory planning of redundant robots performing tasks within an enclosed workspace. Configuration control of kinematically redundant manipulators using the pseudo‐inverse with null‐space projection method is a well‐known scheme. One advantage of this method is that the gradient of an objective function can be included in the homogeneous term to optimize the objective function without affecting the position of the end‐effector. Using different objective functions, this method can achieve redundancy resolution such as obstacle or joint limits avoidance. Along this line of redundancy resolution, a switching objective function is proposed. We modify Liegeois' joint angle availability objective function so that the midpoints of each joint are switched at a series of prespecified key path points for the end‐effector to achieve. These key path points are planned beforehand according to the geometry of the constrained workspace. The trajectory planning problem can then be viewed as a series of proper postures (i.e., midpoints) determination problems at the key path points. The proper postures are determined using a combination of the potential field method and the elastic model method that takes into account joint operating ranges and the motion tendency of the end‐effector. A variable weighting technique to achieve the proper postures effectively is also presented. Simulations of a planar eight‐link robot in a constrained workspace illustrate the effectiveness of the switching objective function with the variable weighting approach in trajectory planning problems. ©1999 John Wiley & Sons, Inc.     

A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

A collision‐avoidance scheme for redundant manipulators: Theory and experiments

The development of a collision‐ and self‐collision‐avoidance scheme for redundant manipulators is discussed in this paper. The method is based on modeling the arm and its environment by simple geometric primitives (cylinders and spheres). A compact method of detecting collisions between two cylinders is introduced. By resorting to the notions of dual angles and dual vectors for representing the axes of cylinders in space, a characterization of different types of collisions is introduced. The performance of the proposed scheme is demonstrated for a seven degrees‐of‐freedom redundant manipulator via simulations and experiments. © 2005 Wiley Periodicals, Inc.     

A new repetitive controller for mechanical manipulators

A new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks is developed. This controller does not require exact knowledge of the manipulator dynamic structure or its parameters, and is computationally efficient. In addition, no actual joint accelerations or any matrix inversions are needed in the control law. The global asymptotic stability of the ideal and the robust stability of the nonideal control system is proven, taking into account the full nonlinear dynamics of the manipulator. Simulation results of this algorithm applied to a realistic Scara type manipulator, which includes dry friction, pay-load inertia variations, actuator/sensor noise, and unmodelled dynamics are also presented.     

A minimization method for boolean functions

Algorithms are proposed for constructing one and all prime implicants covering a given point, a DNF consisting of prime implicants, and a reduced DNF. The complexity of the proposed algorithms is investigated.Translted from Kibernetika, No. 5, pp. 44–48, September–October, 1989.