Redundancy Resolution of Kinematically Redundant Parallel Manipulators Via Differential Dynamic Programing

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
João Cavacanti Santos ◽  
Maíra Martins da Silva
Keyword(s):  
Parallel Manipulators ◽  
Projection Methods ◽  
Inverse Kinematic ◽  
Gradient Projection ◽  
Redundancy Resolution ◽  
Inverse Kinematic Problem ◽  
Serial Manipulators ◽  
Optimal Inputs ◽  
Dynamic Programing ◽  
Gradient Projection Methods

Kinematic redundancy may be an efficient way to improve the performance of parallel manipulators. Nevertheless, the inverse kinematic problem of this kind of manipulator presents infinite solutions. The selection of a single kinematic configuration among a set of many possible ones is denoted as redundancy resolution. While several redundancy resolution strategies have been proposed for planning the motion of redundant serial manipulators, suitable proposals for parallel manipulators are seldom. Redundancy resolution can be treated as an optimization problem that can be solved locally or globally. Gradient projection methods have been successfully employed to solve it locally. For global strategies, these methods may be computationally demanding and mathematically complex. The main objective of this work is to exploit the use of differential dynamic programing (DDP) for decreasing the computational demand and mathematical complexity of a global optimization based on the gradient projection method for redundancy resolution. The outcome of the proposed method is the optimal inputs for the active joints for a given trajectory of the end-effector considering the input limitations and different cost functions. Using the proposed method, the performance of a redundant 3PRRR manipulator is investigated numerically and experimentally. The results demonstrate the capability and versatility of the strategy.

On redundancy resolution and energy consumption of kinematically redundant planar parallel manipulators

Robotica ◽  
2018 ◽  
Vol 36 (6) ◽  
pp. 809-821 ◽  
Author(s):  
Andrés Gómez Ruiz ◽  
João Cavalcanti Santos ◽  
Jan Croes ◽  
Wim Desmet ◽  
Maíra Martins da Silva
Keyword(s):  
Energy Consumption ◽  
Predictive Control ◽  
Energy Efficient ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Control Technique ◽  
Redundancy Resolution ◽  
Inverse Kinematic Problem ◽  
Resolution Scheme ◽  
The Impact

SUMMARYNovel kinematic architectures can be alternatives for designing energy efficient robotic systems. In this work, the impact of kinematic redundancies in the energy consumption of a planar PKM, the 3PRRR manipulator, is experimentally verified. Because of the presence of the kinematic redundancies, the inverse kinematic problem presents infinity solutions. In this way, a redundancy resolution scheme based on the Model Predictive Control technique is proposed and exploited. It can be concluded that the energy consumption of the non-redundant parallel manipulator 3RRR for executing predefined tasks can be considerably reduced by the inclusion of kinematic redundancies.

Exact solution of inverse kinematic problem of 6R serial manipulators using Clifford Algebra

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 417-422 ◽  
Author(s):  
Eriny W. Azmy
Keyword(s):  
Exact Solution ◽  
Clifford Algebra ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Serial Manipulators

SUMMARYIn this paper, Clifford Algebra is used to model and facilitate solving the inverse kinematic problem for robots with only two consecutive parallel axes. It is shown that when a solution exists, it is usually the case that one of the angles of rotation can be arbitrarily chosen from a union of intervals. The remaining angles are then uniquely determined. Of course, there are cases when no solution exists, such as when the object is out of reach. But typically, when solutions exist, there are infinitely many sets of solutions.

Singularity robust balancing of parallel manipulators following inconsistent trajectories

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 2027-2038 ◽  
Author(s):  
Mustafa Özdemir
Keyword(s):  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Type I ◽  
Type Ii ◽  
Inverse Dynamic ◽  
Serial Manipulators ◽  
Dynamic Solution ◽  
Singular Configuration ◽  
Kinematic Singularities

SUMMARYWhen compared to serial manipulators, parallel manipulators have small workspaces mainly due to their closed-loop structure. As opposed to type I singularities (or inverse kinematic singularities) that are generally encountered at the workspace boundaries, type II singularities characteristically arise within the workspace, and around them, the inverse dynamic solution becomes unbounded. Hence, a desired trajectory passing through a type II singular position cannot be achieved by the manipulator, and its useful workspace becomes further and substantially reduced. It has been previously shown in the literature that if the trajectory is replanned in such a way that the dynamic equations of motion of the manipulator are consistent at a type II singularity, i.e. if the trajectory is consistent, then the manipulator passes through this singular configuration in a controllable manner, while the inverse dynamic solution remains finite. An inconsistent trajectory, on the other hand, is stated in the literature to be unrealizable. However, although seems a promising technique, trajectory replanning itself is also a deviation from the originally desired trajectory, and there might be cases in applications where, due to some task-specific reasons, the desired trajectory, although inconsistent, is not allowed to be replanned to satisfy the consistency conditions. In this paper, a method of singularity robust balancing is proposed for parallel manipulators passing through type II singular configurations while following inconsistent trajectories. By this means, an originally unrealizable inconsistent trajectory passing through a type II singularity can be followed without any deviation, while the required actuator forces remain bounded after the manipulator is balanced according to the design methodology presented in this study. The effectiveness of the introduced method is shown through numerical simulations considering a planar 3-DOF 2-PRR parallel manipulator under different balancing scenarios.

scholarly journals Inverse kinematic analysis of 3 DOF 3-PRS PM for machining on inclined prismatic surfaces

2020 ◽  
Vol 9 (2) ◽  
pp. 135
Author(s):  
Hishantkumar Rashmikantbhai Patel ◽  
Yashavant Patel
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Inverse Kinematic ◽  
Medical Surgery ◽  
Space Technology ◽  
Serial Manipulators ◽  
Part Surface ◽  
Primary Focus ◽  
Structural Architecture

<p>Parallel Manipulators (PMs) are family members of modern manipulators based on the closed loop structural architecture. 3-PRS (prismatic, revolute, spherical) manipulator with 3DOF is investigated for its machining capability on prismatic surfaces as it possesses greater structural stiffness, higher pay load caring capacity, more precision compare to serial manipulators as well as less accumulation of errors at joints within a constrained workspace. The said manipulator can be utilized in various fields of application such as precise manufacturing, medical surgery, space technology and many more. In this paper, the primary focus on usage of parallel manipulator in industrial applications such as drilling and grooving on inclined work part surface. Inverse kinematic solutions are used for drilling, square and round profiles on inclined surface using parallel manipulator.</p>

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