Joint trajectory generation for redundant robots in an environment with obstacles

Abstract

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.

Obstacle avoidance planning for redundant manipulator based on variational method

“…The extreme value in variational method can be easily obtained, so it is generally applied to address modern control system problem, such as the minimum energy control, the smallest error control, the shortest time control, the maximum velocity control and the minimum fuel control, etc. [14,15]. In this paper, we solve the excessive joint movement during the process of obstacle avoiding by using the variational method.…”

“…is the end-effector velocity and m R q ∈  is the joint velocity [14,15,16,20]. Therefore, we can obtain the velocity inverse kinematics through the generalize inverse Jacobian matrix method as follows:…”

“…The gradient factor k in velocity inverse kinematics is generally fixed. Considering the fixed gradient projection factor could cause a great difference between the leastnorm solution and homogeneous solution, which may lead to obstacle avoidance failure, this paper uses a 2-norm continuous function as the dynamic gradient projection factor [14,15,16], and it can be represented as:…”

A New Objective Function for Obstacle Avoidance by Redundant Service Robot Arms

“…Prior research addressed obstacle avoidance algorithm designs as a sub-task for redundant robots [10][11][12][13][14][15][16] and a review of null-space. In these studies, the common approach was to first identify the closest points on the links of the redundant robot to the obstacles and then design a sub-task objective function to keep those points away from obstacles.…”

“…In these studies, the common approach was to first identify the closest points on the links of the redundant robot to the obstacles and then design a sub-task objective function to keep those points away from obstacles. In [10] and [11], one stationary obstacle was considered and the objective function to be maximized was chosen as the distance between the links of the redundant robot to avoid a collision. For the case of multiple obstacles, the objective function in [10] and [11] was modified in [12] to be equal to the sum of the minimum distances to each obstacle.…”