Redundancy Resolution via QP Approach and Unification

A redundant manipulator can achieve multiple tasks using the degree of redundancy.In this paper, a redundancy resolution problem is formulated with multiple criteria into a local equality and inequality constrained optimization problem.To achieve multiple tasks, the task with the highest priority can be performed by optimizing a corresponding objective function.The forward kinematic relation and the other tasks with higher priority are performed by satisfying an equality constraint and a set of inequality constraints, respectively.The solution of the path planning is then obtained using an optimization procedure.Different to the conventional approach, the inverse of the Jacobian matrix is not used in the proposed method.The proposed method also provides a unified approach to solve motion planning problems with multiple tasks.

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility. The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described. Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.

This paper presents a novel inverse kinematics global method for a redundant robot manipulator performing a tracking maneuver. The proposed method, based on the choice of appropriate initial joint trajectories that satisfy the kinematic constraints to be used as inputs for a multi-start optimization algorithm, allows for the optimization of different integral cost functions, such as kinetic energy and joint torques norm, and can provide solutions with a variety of constraints, both linear and nonlinear. Furthermore, it is suitable for multi-objective optimization, and it is able to find multiple optima with minimal input from the user, and to solve cyclic trajectories. Problems with a high number of parameters have been addressed providing a sequential version of the method based on successive stages of interpolation. The results of simulations with a three-Degrees-of-Freedom (DOF) redundant manipulator have been compared with a solution available in the literature based on the calculus of variations, thus leading to the validation of the method. Moreover, the effectiveness of the presented method has been shown when used to solve problems with constraints on joint displacement, velocity, torque, and power.

The morphological design of kinematically redundant robotic manipulators is a non-trivial, task-specific process. The availability of redundant degrees of freedom (DOF) affords a redundant manipulator an infinite number of motion solutions for a given task, thereby allowing the achievement secondary manipulation goals. Motion control methods play an integral role in the quality of redundancy resolution, but the degree of resolution attainable by these methods is ultimately determined by morphological design. In this study, a weighted isotropy measure is developed for use in optimising kinematically redundant manipulator design quality. This measure is designed to quantify manipulator performance on multiple secondary motion goals. The measure is employed as a morphological fitness metric for a constrained non-linear morphology optimisation problem. Optimisation results show that using the weighted isotropy measure significantly increased the performance levels of a kinematically redundant manipulator, with respect to secondary manipulation goals, for the intended set of tasks.

The redundant manipulator as a ubiquitous and essential component of robots, acts as a momentous role in mechanized production. The motion control of a redundant manipulator is an essential problem that must be handled. Consequently, for the repetitive motion control of redundant manipulators, a recurrent neural network (RNN) model for the double-index (DI) scheme is researched in this paper. The DI scheme sets the minimum kinetic energy (MKE) and minimum joint-angle offset (MJAO) as optimization indexes, for which the time-dependent weights are designed, and takes the dynamic equations of redundant manipulators and joint limit constraints into consideration as well. Then, the DI scheme is reformulated as a quadratic programming (QP) problem. Besides, the RNN model based on the iteration of related parameters is derived to solve the QP problem, through which joint data (i.e., joint angles, joint velocities, and joint accelerations) are obtained to drive the motion of the redundant manipulator. To verify the effectiveness of the DI scheme for motion control of redundant manipulator, simulation results of the DI scheme solved by the RNN model, the minimum acceleration norm (MAN) scheme and MKE scheme are compared.

In this paper, we introduce a novel and efficient hybrid trajectory planning method for autonomous driving in highly constrained environments. The contributions of this paper are fourfold. First, we present a trajectory planning framework that is able to handle geometry constraints, nonholonomic constraints, and dynamics constraints of cars in a humanlike and layered fashion and generate curvature-continuous, kinodynamically feasible, smooth, and collision-free trajectories in real time. Second, we present a derivative-free global path modification algorithm to extract high-order state information in free space for state sampling. Third, we extend the regular state-space sampling method widely used in on-road autonomous driving systems to a multi-phase deterministic state-space sampling method that is able to approximate complex maneuvers. Fourth, we improve collision checking accuracy and efficiency by using a different car footprint approximation strategy and a two-phase collision checking routine. A range of challenging simulation experiments show that the proposed method returns high-quality trajectories in real time and outperforms existing planners, such as hybrid A* and conjugate-gradient descent path smoother in terms of path quality, efficiency, and computation resources used.

SUMMARYThe evaluation of joint velocity, torque, and power capability of the 8-PSS redundant parallel manipulator is investigated in this paper. A series of new joint capability indices with obvious physical meanings are presented. The torque index used to evaluate the respective joint dynamic capability of the redundant parallel manipulator is decoupled into the acceleration, velocity, and gravity term. With these velocity, torque, and power indices, it is possible to control the respective joint capability of the redundant parallel manipulator in different directions. The indices have been applied to evaluate the joint capability of the redundant parallel manipulator by simulation. They are general and can be used for other types of parallel manipulators.

Fault-tolerant motion planning and control of redundant manipulator

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.

Closed-loop inverse kinematics (CLIK) algorithm mostly resolves the redundancy at the velocity level. In this paper we extend the CLIK algorithm to the acceleration level to meet some applications that require the joint accelerations. The redundancy resolutions at the velocities and acceleration levels via pseudoinverse method are analyzed respectively. The objective function of joint limits avoidance(JLA) is combined into the redundancy resolution as an optimization approach of the null space motion. A seven-DOF redundant manipulator is designed to do the computer simulations and the real experiments are carried out on a Powercube modular manipulator. Their results demonstrated the effectiveness of the proposed algorithm.

This paper addresses the task space impedance control of a robot driven through the multistage nonlinear flexible transmission. The proposed controller uses limited information of the angle and the current of the motors to regulate the end point compliance at the specified set point. In particular, motor angle is employed to estimate the stationary robot link angle and joint velocity in real time. They are then used to constitute the stationary force on the attempt to cancel the robot gravity force and to form the task space interacting force according to the desired impedance characteristics. Motor current is used to infer the transmitted torque to the robot. This torque is fed back to mitigate the effect of the motor inertia from deteriorating the desired impedance. Asymptotic stability of this controller with the flexible joint robot is guaranteed with additional damping. Passivity of the system is also investigated. Simulation and experiments of the proposed control scheme on a two degrees-of-freedom (DOF) cable-pulley driven flexible joint robot model are examined.

Redundant manipulators are characterized by a high number of degrees of freedom (DOF) than the required number to perform a given task. This additional DOF of the robot enhances it to work in the cluttered environment by avoiding obstacles and provides improved dexterity while performing a given task. Inverse Kinematics (IK) of redundant manipulators has infinite solutions. Among these infinite solutions, only those solutions are preferred which fulfill the criteria such as joint distance minimization, singularity avoidance, and joint torque minimization. This paper focuses on the IK of redundant manipulators for a given path with secondary objectives as performance criteria. The IK problem is formulated as an optimization problem by choosing the joint distance and singularity avoidance as objectives and collision with obstacles in the workspace as constraints. Simulations have been performed on serial redundant manipulators by varying different types of obstacles and their positions in the workspace. Results are also reported on redundancy resolution of serial manipulators based on singularity avoidance criterion.

An increasingly important trend is to simulate a human arm using a 7-degrees-of-freedom (DOF) redundant manipulator and accomplish complex tasks in an unstructured environment by leveraging human experience. Human arm motion information acquired by a biomimetic motion capture system is mapped to planning information of the manipulator to leverage human experience in the control process and quickly improve the operational capability of the manipulator in complex environments. In this paper, extensive tests are performed for verification, and the test results prove the effectiveness of the proposed algorithm, which improve the operational performance of a redundant manipulator in a complex environment to accomplish humanoid tasks and is critical to robot-aided operations or the complete substitution of humans by robots in the future.

In this paper the problem of planning trajectories using human-like vision information, and of solving inverse kinematics of robots by weighting joint involvement in a biomimetic fashion is considered. Movements of a redundant seven degree-of-freedom (DOF) robot manipulator, having a kinematic structure similar to that of the human arm, have been simulated. The design of the trajectory is based on theory about attentive vision in humans, and biomimetic considerations are used to infer laws to obtain human-like movements in inverse kinematics. The inverse kinematics is computed using a closed-loop algorithm with redundancy resolution where physically motivated secondary tasks are imposed to the internal motions, with the virtual end-effectors approach. Outputs of the IK algorithm related to drawing trajectories in the task space are compared with the positions of the joints of a human performing the same drawing task, computed from the images caught by a three-camera system

The human arm is kinematically redundant with respect to reaching tasks in a 3 dimensional (3D) workspace. Research on reaching movements of the healthy human arm reveals the control strategy of the human motor system, which can be further applied to the upper limb exoskeletons used for stroke rehabilitation. Experiments performed on ten healthy subjects have shown that when reaching from one point to another, the human arm rotates around an axis going through the shoulder. The proposed redundancy resolution based on the direction of the axis can predict the arm posture with a higher accuracy comparing to a redundancy resolution that maximizes the motion efficiency. It is also shown that for reaching movements in the comfortable arm motion range, the directions of the axis are constrained by a linear model.