The Modular Nonoverlapping Grasp Workspaces and Dynamics for the Grippers using the Micro and Macro C-Manifold Design

The toolbox for the gripper workspace analyses using Lie algebra is developed for shape variables (α1-4 − θ1,2) of the skew revolute joints. The unique methodology for grippers comprises to enable the variety of manifold analyses for kinematics and dynamics using symbolic mathematics. The Controllable Instantaneous Screw Axes (C-ISA) are defined through the shape variables considering the twists of the skew revolute joints se(3). The derivation and analyses of the kinematics and dynamics equations are made possible using the developed methodology with the defined constraints for gripper mechanisms. The Modular Gripper with Lie Algebra Toolbox (M-GLAT) is developed for the defined constraints of the angle between C-ISA 1 and C-ISA 2. The novelty subject of this article is the development of the M-GLAT method for derivation of the constraint based workspaces with the shape variables (α1-4 − θ1,2) in the field of the spatial 2-RR gripper mechanisms. The gripper dynamics with constraint based workspaces of the skew revolute joints are developed for varied configurations of α1-4 with ICs of θ1,2. The modular rule-based workspaces are analyzed for the shape variables of the (α1‑4 − θ1,2) with the task spaces. This design produces dexterity with the modular grasp workspaces for the gripper fingers with skew revolute joints. One can select a combination of C-manifolds of (π/20, π/40, π/80) for the requirement of the nonoverlapping workspaces of the gripper finger designs as the grasp surfaces to control.  The modular nonoverlapping workspace design with dynamics herein is based on the shape variables (α1-4 − θ1,2) using skew revolute joint which produce the high dexterity for the grasping capability of the grippers. The modular micro and macro C-manifold designs obtained the constraint based workspace algorithms of the 2-RR gripper which is expandable into the higher modular revolute joints of the n-R for the grippers. The n-R modular expandable grippers are increasing the precision and power grasping capability

The Modular Nonoverlapping Grasp Workspaces and Dynamics for the Grippers using the Micro and Macro C-Manifold Design

766-776The toolbox for the gripper workspace analyses using Lie algebra is developed for shape variables (α1-4 − θ1,2) of the skew revolute joints. The unique methodology for grippers comprises to enable the variety of manifold analyses for kinematics and dynamics using symbolic mathematics. The Controllable Instantaneous Screw Axes (C-ISA) are defined through the shape variables considering the twists of the skew revolute joints se(3). The derivation and analyses of the kinematics and dynamics equations are made possible using the developed methodology with the defined constraints for gripper mechanisms. The Modular Gripper with Lie Algebra Toolbox (M-GLAT) is developed for the defined constraints of the angle between C-ISA 1 and C-ISA 2. The novelty subject of this article is the development of the M-GLAT method for derivation of the constraint based workspaces with the shape variables (α1-4 − θ1,2) in the field of the spatial 2-RR gripper mechanisms. The gripper dynamics with constraint based workspaces of the skew revolute joints are developed for varied configurations of α1-4 with ICs of θ1,2. The modular rule-based workspaces are analyzed for the shape variables of the (α1-4 − θ1,2) with the task spaces. This design produces dexterity with the modular grasp workspaces for the gripper fingers with skew revolute joints. One can select a combination of C-manifolds of (π/20, π/40, π/80) for the requirement of the nonoverlapping workspaces of the gripper finger designs as the grasp surfaces to control. The modular nonoverlapping workspace design with dynamics herein is based on the shape variables (α1-4 − θ1,2) using skew revolute joint which produce the high dexterity for the grasping capability of the grippers. The modular micro and macro C-manifold designs obtained the constraint based workspace algorithms of the 2-RR gripper which is expandable into the higher modular revolute joints of the n-R for the grippers. The n-R modular expandable grippers are increasing the precision and power grasping capability

Task-Based Motion Planning Using Optimal Redundancy for a Minimally Actuated Robotic Arm

In planning robotic manipulations, heuristic searches are commonly considered impractical due to the high dimensionality of the problem caused by redundancy in the kinematic chain. In this paper, we present an optimal motion planning algorithm for an overly redundant minimally actuated serial robot (MASR) using the manipulator workspace as a foundation for the heuristic search. By utilizing optimized numerical probability methods, a novel sub-workspace search was developed. The sub-workspace allows the search to quickly and accurately find the minimal sub-set of joints to be actuated and ensures the existence of a path to a given target. Further on, the search result is used as a search graph for the heuristic planning problem which guarantees an optimal solution within the problem boundaries. Using this approach, optimal heuristic search can become practical for various types of manipulators, tasks, and environments. We describe our workspace minimization and heuristic search using the example of a general robotic arm and then implement the approach on a MASR model, a robotic arm with five passive joints and a single mobile actuator that is free to travel along the arm and rotate each joint separately. A series of simulations show how our minimal redundancy approach can benefit from path planning in the case of traditional hyper-redundant manipulators, and its greater effectiveness when addressing the specific design of the MASR

Task-Based Motion Planning Using Optimal Redundancy for a Minimally Actuated Robotic Arm

In planning robotic manipulations, heuristic searches are commonly considered impractical due to the high dimensionality of the problem caused by redundancy in the kinematic chain. In this paper, we present an optimal motion planning algorithm for an overly redundant minimally actuated serial robot (MASR) using the manipulator workspace as a foundation for the heuristic search. By utilizing optimized numerical probability methods, a novel sub-workspace search was developed. The sub-workspace allows the search to quickly and accurately find the minimal sub-set of joints to be actuated and ensures the existence of a path to a given target. Further on, the search result is used as a search graph for the heuristic planning problem which guarantees an optimal solution within the problem boundaries. Using this approach, optimal heuristic search can become practical for various types of manipulators, tasks, and environments. We describe our workspace minimization and heuristic search using the example of a general robotic arm and then implement the approach on a MASR model, a robotic arm with five passive joints and a single mobile actuator that is free to travel along the arm and rotate each joint separately. A series of simulations show how our minimal redundancy approach can benefit from path planning in the case of traditional hyper-redundant manipulators, and its greater effectiveness when addressing the specific design of the MASR