Real-time inverse kinematics of redundant manipulators using neural networks and quadratic programming

A general method is presented for the inverse kinematics resolution of redundant manipulators with joint limits. The success of avoiding joint angular position limits of the original clamping weighted least-norm method is ascribable to the strength of the repulsive potential field function. However, the repulsive potential field function may lead to excessive joint angular velocities that can exceed the corresponding limits. We propose an improved clamping weighted least-norm method that adds an elastic field function into the original method for the sake of sustaining the constraints of joint angular velocity limits. Moreover, for hierarchical task-level construction, the priority of avoiding joint angular velocity limits is lower than that of avoiding joint angular position limits. To adequately illustrate the effectiveness of the proposed method, case studies were performed in comparison with other methods in singular configurations of a redundant manipulator.

A study on avoiding joint limits for inverse kinematics of redundant manipulators using improved clamping weighted least-norm method

In this paper, a hybrid trajectory tracking controller is designed for redundant robot manipulators, consisting of RBF neural network and an adaptive bound on disturbances. The controller is composed of computed torque type part, RBF neural network and an adaptive controller. The controller achieves end-effector trajectory tracking as well as subtask tracking effectively. The controller is able to learn the existing structured and unstructured uncertainties in the system in online manner. The RBF network learns the unknown part of the robot dynamics with no requirement of the offline training. The adaptive controller is used to estimate the unknown bounds on unstructured uncertainties and neural network reconstruction error. The overall system is proved to be asymptotically stable in the sense of Lyapunov. Finally, numerical simulation studies are performed on a 3R planar robot manipulator to show the effectiveness of the control scheme.

Tracking control of redundant robot manipulators using RBF neural network and an adaptive bound on disturbances

Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK) resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA) as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the c...

https://journals.sagepub.com/doi/pdf/10.5772/63934

Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm

In this paper, a numerical method based on neural network is presented to solve inverse kinematics problem of redundant manipulators subject to joint angle limits and obstacles in the workspace of the robot. The proposed method is performed in real time, where radial-basis function neural network is used to obtain joint angles of the robot. In order to satisfy constrains, a method called Nonlinear Quadratic Programming (NQP) is applied to update NN's weights. Moreover, it will be shown that if the Kuhn-Tucker conditions are satisfied, then convergence of NN's weights is guaranteed. Since the process is performed on-line, the computational time of obtaining the inverse kinematics solution must be suitable for real-time applications such as control of the robot manipulators. Moreover, since the convergence rate of the problem depends on the initial weights of the neural network, several initial weights are used relative to suitable factors such as feasibility of the solution and vicinity of the desired point. Simulations are carried out on the PA-10 redundant manipulator to show effectiveness of the proposed algorithm.

Kinematic control of a seven DOF robot manipulator with joint limits and obstacle avoidance using neural networks

In this paper, we develop a control of a redundant robot manipulator. That has to carry out a trajectory tracking in operational space while avoiding an obstacle. For this purpose, extended Jacobian method is used. The Self-motion vector is introduced at the level of the inverse kinematic solution in order to produce the obstacle avoidance (the secondary task). Thus, robot avoids obstacles without influencing the main task (trajectory tracking). The self-motion is computed from the optimization of scalar function depending on an anti collision constraint. Finally, this control method has leaded to a trajectory tracking in Cartesian space while avoiding the obstacle.

H. Chekireb

Papers

Redundant robot manipulator control with obstacle avoidance using extended Jacobian method