Collision Avoidance of Redundant Robotic Manipulators Using Newton’s Method

Abstract

This study investigates the application of Newton method to the problems of collision avoidance and path planning for robotic manipulators, especially robots with high Degrees of Freedom (DOF). The proposed algorithm applies to the potential fields method, where the Newton technique is used for performing the optimization. As compared to classical gradient descent method this implementation is mathematically elegant, enhances the performance of motion generation, eliminates oscillations, does not require gains tuning, and gives a faster convergence to the solution. In addition, the paper presents a computationally efficient symbolic formula for calculating the Hessian with respect to joint angles, which is essential for achieving realtime performance of the algorithm in high DOF configuration spaces. The method is validated successfully in simulation environment. Results for different methods (Newton, gradient descent and gradient descent with momentum) are compared in terms of quality of the path generated, oscillations, minimum distance to obstacles and convergence rate.

Collision-free kinematics for hyper-redundant manipulators in dynamic scenes using optimal velocity obstacles

“…Other recent optimization methods studied are based on curve-constrained collision-free trajectory control, 35 vector field inequalities, 36 and Newton's method. 37…”

“…It can be observed that the algorithms in the literature 17,39 do not consider the obstacles in the workspaces. In the literature, 7,15,18,33,37 although the proposed approaches can avoid collisions, they cannot be applied to the dynamic working environments. Moreover, the algorithms in Rolf et al 17 and Safeea et al 37 only apply to 2D workspaces.…”

“…In the literature, 7,15,18,33,37 although the proposed approaches can avoid collisions, they cannot be applied to the dynamic working environments. Moreover, the algorithms in Rolf et al 17 and Safeea et al 37 only apply to 2D workspaces. Note that the proposed algorithm can compute the collision-free inverse kinematic solutions in dynamic workspaces and can handle hyper-redundant manipulators.…”

A Collision Avoidance Strategy for Redundant Manipulators in Dynamically Variable Environments: On-Line Perturbations of Off-Line Generated Trajectories

“…The same principle of repulsive velocities generated by obstacles can be used in order to avoid collisions between obstacles and control points along the kinematic chain of the manipulator: in addition to the motion imposed on the end-effector, a repulsive velocity vector can be applied to the point of the robot that is closer to one of the obstacles, adding a task to the control system [15][16][17][18][19]. Specifying some studies, a comprehensive work can be found in [2], where a kinematic control for on-line obstacle avoidance in a redundant manipulator is proposed and an approximated and computationally efficient solution for the pseudoinverse is used to manage the redundancy of the manipulator; in [5], a grid-based distance-propagating dynamic system is adopted, where penalty functions are used to generate safety margins around the obstacles.…”

“…whereẋ c =ẋ e + ke is the corrected end-effector velocity, k the positive gain and e is the position error between the desired position x e and the actual position x. The first term of Equation (16) guarantees the exact velocity of the end effector with a minimum joint speed.…”