Redundancy analysis of cooperative dual-arm manipulators

Abstract

This paper presents the redundancy analysis of two cooperative manipulators, showing how they can be considered as a single redundant manipulator through the use of the relative Jacobian matrix. In this way, the kinematic redundancy can be resolved by applying the principal local optimization techniques used in the single manipulator case. We resolve the redundancy by using the Jacobian null space technique, which permits us to perform several tasks with different execution priority levels at the same time; this is a useful feature, especially when the manipulators are to be mounted on and cooperate with a mobile platform. As an illustrative example, we present a case study consisting of two planar manipulators mounted on a smart wheelchair, whose degrees of redundancy are employed to move an object along a predefined path, while avoiding an obstacle in the manipulator's workspace at the same time.

Dual-arm cooperative manipulation based on differential evolution

“…The penalty function defined in equation 6 handles constraints when q l i < q i . On the other hand, the penalty function given in equation (5) handles constraints when q i < q u i .…”

“…Redundancy in robotic manipulators is a very important problem to solve. Generally, a single-arm system is defined as kinematically redundant when its degree of motion n (number of joints) is higher than the number of variables m that are necessary to perform a given task (dimension of the task), this is n > m. 5 Since a dual-arm manipulation of a rigid object form a closed kinematic chain, then dual-arm systems are considered kinematically redundant. 1,8 Redundancy solutions admit several joints configuration to reach the same desired end-effector pose, in consequence, the inverse kinematics becomes difficult to solve.…”

Dual-arm cooperative manipulation under joint limit constraints

“…where J i † (i = 1, 2, 3) is the pseudo inverse of the Jacobian of each task, while P j (j = 2, 3) indicates the orthogonal projector on the null space N j , that is obtained by I − J † j J j (where I indicates the identity matrix). As proposed in [11,28], in the dual arm system based on the Jacobian null space projection, we set the highest priority task to retain motion coordination 210 represented by˙ x R d k , while the secondary task is given by the desired A e motioṅ x A d k , which is expressed with respect to its base frame A b . Moreover, if the system possesses redundant motions, in accordance with (9), it is possible to add a third task in order to satisfy further constraints (e.g., increasing the system manipulability [29] or avoiding joint position limits [28]).…”

“…As proposed in [11,28], in the dual arm system based on the Jacobian null space projection, we set the highest priority task to retain motion coordination 210 represented by˙ x R d k , while the secondary task is given by the desired A e motioṅ x A d k , which is expressed with respect to its base frame A b . Moreover, if the system possesses redundant motions, in accordance with (9), it is possible to add a third task in order to satisfy further constraints (e.g., increasing the system manipulability [29] or avoiding joint position limits [28]). Since the study in 215 this paper is focused on the joint limits avoidance, it can be expressed as a repulsive joint velocity vector˙ q + k , which pushes the joint positions away from their limits.…”

Inverse kinematics for cooperative mobile manipulators based on self-adaptive differential evolution

“…Consequently, a cooperative mobile manipulator system is considered redundant. Redundancy occurs when the degree of motion is higher than the number of necessary variables to perform a task (Freddi et al, 2016). The inverse kinematics for redundant robots becomes difficult to solve because redundancy admits several joint configurations to reach the same end-effector pose.…”