Inverse kinematics of redundant manipulators with guaranteed performance

Robotica ◽  
2021 ◽  
pp. 1-21
Author(s):  
Dongsheng Guo ◽  
Aifen Li ◽  
Jianhuang Cai ◽  
Qingshan Feng ◽  
Yang Shi
Keyword(s):  
Path Planning ◽  
Obstacle Avoidance ◽  
Discrete Time ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Superior Performance ◽  
Redundant Manipulators ◽  
End Effector ◽  
Great Performance ◽  
Time Form

Abstract In this paper, the inverse kinematics (IK) of redundant manipulators is presented and studied, where the performance of end-effector path planning is guaranteed. A new Jacobian pseudoinverse (JP)-based IK method is proposed and studied using a typical numerical difference rule to discretize the existing IK method based on JP. The proposed method is depicted in a discrete-time form and is theoretically proven to exhibit great performance in the IK of redundant manipulators. A discrete-time repetitive path planning (DTRPP) scheme and a discrete-time obstacle avoidance (DTOA) scheme are developed for redundant manipulators using the proposed method. Comparative simulations are conducted on a universal robot manipulator and a PA10 robot manipulator to validate the effectiveness and superior performance of the DTRPP scheme, the DTOA scheme, and the proposed JP-based IK method.

scholarly journals Hybrid Mutation Fruit Fly Optimization Algorithm for Solving the Inverse Kinematics of a Redundant Robot Manipulator

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jianping Shi ◽  
Yuting Mao ◽  
Peishen Li ◽  
Guoping Liu ◽  
Peng Liu ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Fruit Fly ◽  
Fruit Fly Optimization Algorithm ◽  
Redundant Manipulators ◽  
End Effector ◽  
Redundant Robot ◽  
Fruit Fly Optimization ◽  
Inverse Kinematics Problem

The inverse kinematics of redundant manipulators is one of the most important and complicated problems in robotics. Simultaneously, it is also the basis for motion control, trajectory planning, and dynamics analysis of redundant manipulators. Taking the minimum pose error of the end-effector as the optimization objective, a fitness function was constructed. Thus, the inverse kinematics problem of the redundant manipulator can be transformed into an equivalent optimization problem, and it can be solved using a swarm intelligence optimization algorithm. Therefore, an improved fruit fly optimization algorithm, namely, the hybrid mutation fruit fly optimization algorithm (HMFOA), was presented in this work for solving the inverse kinematics of a redundant robot manipulator. An olfactory search based on multiple mutation strategies and a visual search based on the dynamic real-time updates were adopted in HMFOA. The former has a good balance between exploration and exploitation, which can effectively solve the premature convergence problem of the fruit fly optimization algorithm (FOA). The latter makes full use of the successful search experience of each fruit fly and can improve the convergence speed of the algorithm. The feasibility and effectiveness of HMFOA were verified by using 8 benchmark functions. Finally, the HMFOA was tested on a 7-degree-of-freedom (7-DOF) manipulator. Then the results were compared with other algorithms such as FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA. The pose error of end-effector corresponding to the optimal inverse solution of HMFOA is 10−14 mm, while the pose errors obtained by FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA are 102 mm, 10−1 mm, 10−2 mm, 102 mm, and 102 mm, respectively. The experimental results show that HMFOA can be used to solve the inverse kinematics problem of redundant manipulators effectively.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

Redundancy utilization for obstacle avoidance of planar robot manipulators

1997 ◽  
Vol 211 (6) ◽  
pp. 463-475 ◽  
Author(s):  
U Sezgin ◽  
L D Seneviratne ◽  
S W E Earles
Keyword(s):  
Obstacle Avoidance ◽  
Computer Simulations ◽  
Redundant Manipulators ◽  
Control Points ◽  
Kinematic Redundancy ◽  
End Effector ◽  
Revolute Joints ◽  
Planar Robot ◽  
And Control ◽  
Configuration Control

Two obstacle avoidance criteria are developed, utilizing the kinematic redundancy of serial redundant manipulators having revolute joints and tracking pre-determined end effector paths. The first criterion is based on the instantaneous distances between certain selected points along the manipulator, called configuration control points (CCP), and the vertices of the obstacles. The optimized joint configurations are obtained by maximizing these distances. Thus, the links of the manipulator are configured away from the obstacles. The second criterion uses a different approach, and is based on Voronoi boundaries representing the equidistant paths between two obstacles. The optimized joint configurations are obtained by minimizing the distances between the CCP and control points selected on the Voronoi boundaries. The validities of the criteria are demonstrated through computer simulations.

Redundancy Parameterization for Flexible Motion Control

2010 ◽  
Author(s):  
B. Moore ◽  
E. Oztop
Keyword(s):  
Finite Number ◽  
Inverse Kinematics ◽  
Infinitely Many Solutions ◽  
Redundant Manipulators ◽  
Real Time Control ◽  
End Effector ◽  
Human Control ◽  
Time Control ◽  
Swivel Angle ◽  
Self Motion

Our overall research interest is in synthesizing human like reaching and grasping using anthropomorphic robot hand-arm systems, as well as understanding the principles underlying human control of these actions. When one needs to define the control and task requirements in the Cartesian space, the problem of inverse kinematics needs to be solved. For non-redundant manipulators, a desired end-effector position and orientation can be achieved by a finite number of solutions. For redundant manipulators however, there are in general infinitely many solutions where the cardinality of the solution set must be made finite by imposing certain constraints. In this paper, we consider the Mitsubishi PA10 manipulator which is similar to the human arm, in the sense that both wrist and shoulder joints can be considered to emulate a 3DOF ball joint. We explicitly derive the analytic solution for the inverse kinematics using quaternions. Then, we derive a parameterization in terms of a pure quaternion called the swivel quaternion. The swivel quaternion is similar to the elbow swivel angle used in most approaches, but avoid the computation of inverse trigonometric functions. This parameterization of the self-motion manifold is continuous with any end-effector motion. Given the pose of the end-effector and the swivel quaternion (or swivel angle), the algorithm derives all solution of the inverse kinematics (finite number). We then show how the parameterization of the elbow self-motion can be used for the real-time control of the PA10 manipulator in the presence of obstacles.

scholarly journals Obstacle Avoidance Techniques for Robot Path Planning

2019 ◽  
Vol 12 (1) ◽  
pp. 56-65
Author(s):  
Ali N. Abdulnabi
Keyword(s):  
Path Planning ◽  
Obstacle Avoidance ◽  
Robot Manipulator ◽  
Optimal Path ◽  
Initial Point ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Robot Arm ◽  
Starting Position ◽  
Elapsed Time

This paper presents a collision-free path planning approaches based on Bézier curve and A-star algorithm for robot manipulator system. The main problem of this work is to finding a feasible collision path planning from initial point to final point to transport the robot arm from the preliminary to the very last within the presence of obstacles, a sequence of joint angles alongside the path have to be determined. To solve this problem several algorithms have been presented among which it can be mention such as Bug algorithms, A-Star algorithms, potential field algorithms, Bézier curve algorithm and intelligent algorithms. In this paper obstacle avoidance algorithms were proposed Bézier and A-Star algorithms, through theoretical studies and simulations with several different cases, it's found verify the effectiveness of the methods suggested. It's founded the Bézier algorithm is smoothing accurate, and effective as compare with the A-star algorithm, but A-star is near to shortest and optimal path to free collision avoidance. The time taken and the elapsed time to traverse from its starting position and to reach the goal are recorded the tabulated results show that the elapsed time with different cases to traverse from the start location to destination using A-star Algorithm is much less as compared to the time taken by the robot using Bézier Algorithm to trace the same path. The robot used was the Lab-Volt of 5DOF Servo Robot System Model 5250 (RoboCIM5250)

Obstacle avoidance inverse kinematics solution of redundant robots by neural networks

Robotica ◽  
1997 ◽  
Vol 15 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Ziqiang Mao ◽  
T. C. Hsia
Keyword(s):  
Neural Network ◽  
Obstacle Avoidance ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Solution Technique ◽  
Training Algorithms ◽  
Neural Network Approach ◽  
Work Space ◽  
The Neural Network ◽  
Free Case

This paper investigates the neural network approach to solve the inverse kinematics problem of redundant robot manipulators in an environment with obstacles. The solution technique proposed requires only the knowledge of the robot forward kinematics functions and the neural network is trained in the inverse modeling manner. Training algorithms for both the obstacle free case and the obstacle avoidance case are developed. For the obstacle free case, sample points can be selected in the work space as training patterns for the neural network. For the obstacle avoidance case, the training algorithm is augmented with a distance penalty function. A ball-covering object modeling technique is employed to calculate the distances between the robot links and the objects in the work space. It is shown that this technique is very computationally efficient. Extensive simulation results are presented to illustrate the success of the proposed solution schemes. Experimental results performed on a PUMA 560 robot manipulator is also presented.

Collision-free path planning of a novel reconfigurable mobile parallel mechanism

2016 ◽  
Vol 231 (20) ◽  
pp. 3728-3742 ◽  
Author(s):  
Pouria Nozari Porshokouhi ◽  
Mehdi Tale Masouleh ◽  
Hossein Kazemi
Keyword(s):  
Path Planning ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
End Effector ◽  
Planning Algorithm ◽  
Repulsive Forces ◽  
Path Planning Algorithm

This paper initially deals with the design of a new customized reconfigurable mobile parallel mechanism. This mechanism is called the ‘Taar Reconfigurable ParaMobile’ (TRPM), consisting of three mobile robots as the main actuators. Then, the kinematics and path planning for this mechanism are presented. The newly proposed mechanism is expected to circumvent some shortcomings of inspection operation in unknown environments with unexpected changes in their workspace, for example, in a water pipe with a non-uniform cross-sectional area. In this paper, ‘Artificial Potential Field’ (APF) has been assumed to be the path planning algorithm and its resulting attractive and repulsive forces are only applied to the end-effector to generate the desired path. It is worth mentioning that the obstacle considered in this paper is a wedge which models an environment with non-uniform cross-sectional area along the path travelled by the end-effector. The inverse kinematics of the TRPM is then solved by resorting to the Resultant method as well as the Homotopy continuation method. The objective of utilizing these two well-known methods is to verify the correctness of the upper bound of solutions. It should be mentioned that solving the inverse kinematic problem obtained from both above-mentioned methods, leads to 12 solutions: eight real and four complex solutions. As a novel parallel mechanism, the TRPM yields a three-degrees-of-freedom kinematic redundancy. Despite the fact that the redundancy is sometimes beneficial for the control procedure, solving the inverse kinematics of the TRPM would be feasible only by adding some constraints. As a result, there will be a system of equations consisting of three kinematic equations and three auxiliary equations. Results from this study reveal that, by applying APF as the path planning algorithm to the TRPM, it is possible to track proper paths to reach the target.

Obstacle Avoidance Path Planning for Harvesting Robot Manipulator Based on MAKLINK Graph and Improved Ant Colony Algorithm

2014 ◽  
Vol 530-531 ◽  
pp. 1063-1067 ◽  
Author(s):  
Wei Ji ◽  
Jun Le Li ◽  
De An Zhao ◽  
Yang Jun
Keyword(s):  
Path Planning ◽  
Obstacle Avoidance ◽  
Ant Colony Algorithm ◽  
Robot Manipulator ◽  
Ant Colony ◽  
Dijkstra Algorithm ◽  
Short Time ◽  
Vector Description ◽  
Harvesting Robot ◽  
Improved Ant Colony Algorithm

To the problems of real-time obstacle avoidance path planning for apple harvesting robot manipulator in dynamic and unstructured environment, a method based on improved ant colony algorithm is presented. Firstly, Vector description is utilized to describe the area where obstacles such as branches is located as irregular polygon in free space, and MAKLINK graph is used to build up the environment space model. Then, the improved Dijkstra algorithm is used to find the initial walk path for apple harvesting robot manipulator. Finally, the improved ant colony algorithm is applied to optimize the initial path. The experiment result shows that the proposed method is simple and the robot manipulator can avoid the branches to pick the apple successfully in a relatively short time.

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