A Geometric Approach to Hyper-Redundant Manipulator Obstacle Avoidance

1992 ◽  
Vol 114 (4) ◽  
pp. 580-585 ◽  
Author(s):  
G. S. Chirikjian ◽  
J. W. Burdick
Keyword(s):  
Differential Geometry ◽  
Obstacle Avoidance ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Redundant Robots ◽  
Geometric Algorithm

The term hyper-redundant refers to redundant manipulators with a very large or infinite number of degrees of freedom. These manipulators are analogous in morphology to snakes, elephant trunks, and tentacles. While a variety of obstacle avoidance algorithms for nonredundant and mildly redundant manipulators exist, little analysis has been performed for hyper-redundant robots. This paper presents a strictly geometric algorithm for hyper-redundant manipulator obstacle avoidance which relies on the use of “tunnels” in the obstacle-filled workspace. Methods of differential geometry are used to formulate equations which guarantee that sections of the manipulator are confined to the tunnels, and therefore avoid obstacles. A general formulation is presented with an example to illustrate this approach.

scholarly journals Redundancy Resolution Using Tractrix: Simulations and Experiments

2009 ◽  
Author(s):  
V. C. Ravi ◽  
Subrata Rakshit ◽  
Ashitava Ghosal
Keyword(s):  
Degrees Of Freedom ◽  
Redundancy Resolution ◽  
Redundant Manipulator ◽  
End Effector ◽  
Redundant Robots ◽  
Natural Motion ◽  
Fixed Base ◽  
Effective Use ◽  
Actuated Joints ◽  
Present Simulation

Hyper-redundant robots are characterized by the presence of a large number of actuated joints, many more than the number required to perform a given task. These robots have been proposed and used for many application involving avoiding obstacles or, in general, to provide enhanced dexterity in performing tasks. Making effective use of the extra degrees of freedom or resolution of redundancy have been an extensive topic of research and several methods have been proposed in literature. In this paper, we compare three known methods and show that an algorithm based on a classical curve called the tractrix leads to a more ‘natural’ motion of the hyper-redundant robot with the displacements diminishing from the end-effector to the fixed base. In addition, since the actuators at the base ‘see’ the inertia of all links, smaller motion of the actuators nearer to the base results in a smoother motion of the end-effector as compared to other two approaches. We present simulation and experimental results performed on a prototype eight link planar hyper-redundant manipulator.

Dynamic Control of Curve-Constrained Hyper-Redundant Manipulators

2004 ◽  
Vol 16 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Shugen Ma ◽  
◽  
Mitsuru Watanabe ◽  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Control ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Real Time Control ◽  
Feed Forward ◽  
Manipulator Dynamics ◽  
Time Control ◽  
Control Scheme ◽  
Feed Forward Controller

Hyper-redundant manipulators have high number of kinematic degrees of freedom, and possess unconventional features such as the ability to enter narrow spaces while avoiding obstacles. To control these hyper-redundant manipulators accurately, manipulator dynamics should be considered. This is, however, time-comsuming and makes implementation of real-time control difficult. In this paper, we propose a dynamic control scheme for hyper-redundant manipulators, which is based on analysis in defined posture space where three parameters were used to determine the manipulator posture. Manipulator dynamics are modeled on the parameterized form with the parameter of the posture space path. The posture space path-tracking feed-forward controller is then formulated on the basis of a parameterized dynamic equation. Computer simulation, in which a hyper-redundant manipulator traces the posture space path well by using the proposed feed-forward controller, proved that the hyper-redundant manipulator tracks the workspace path accurately.

The conceptual design of a spatial binary hyper redundant manipulator and its forward kinematics

2011 ◽  
Vol 226 (1) ◽  
pp. 217-227 ◽  
Author(s):  
A Bayram ◽  
M Kemal Özgören
Keyword(s):  
Conceptual Design ◽  
Degrees Of Freedom ◽  
Forward Kinematics ◽  
Redundant Manipulators ◽  
Variable Geometry ◽  
Redundant Manipulator ◽  
Stable States ◽  
The Third ◽  
Discrete Nature ◽  
Pneumatic Cylinders

The hyper redundant manipulators (HRMs) have excessively many degrees of freedom. As a special but practicable subset of them, the binary hyper-redundant manipulators (BHRMs) use binary (on–off) actuators with only two stable states such as pneumatic cylinders and/or solenoids. This article describes the conceptual design of a spatial BHRM together with its forward kinematics. This BHRM consists of many modules with the same constructive characteristics. The modules increase in size from the tip to the base so that the actuator powers also increase in the same order. Each module consists of three submodules. The first and second submodules have the shapes of variable geometry trusses and they work in mutually orthogonal planes. The third submodule is a discrete twister. The manipulator is assumed to be driven by pneumatic on–off actuators. Because of the discrete nature of the on–off actuators, a small but continuously actuated six-joint manipulator is installed as the last module of the BHRM in order to compensate the discretization errors.

scholarly journals Obstacle avoidance and multitarget tracking of a super redundant modular manipulator based on Bezier curve and particle swarm optimization

2020 ◽  
Author(s):  
Chen Li ◽  
Ying Ma ◽  
Yu Zhang ◽  
Jinguo Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Obstacle Avoidance ◽  
Trajectory Tracking ◽  
Degrees Of Freedom ◽  
Optimization Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Redundant Manipulator ◽  
Swarm Optimization ◽  
Composite Optimization

Abstract A super redundant serpentine manipulator has slender structure and multiple degrees of freedom and can travel through narrow space and move in complex space. This manipulator is composed of many modules that can form different lengths of robot arms for different application sites. The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space. This paper presents a composite optimization method of path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator. In this composite optimization, path planning is established on a Bezier curve, particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator, and a feasible obstacle avoidance path is obtained along with a discrete trajectory tracking using a follow-the-leader strategy. The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve. Simulation results show that this composite optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints. The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.

A Comparison of Continuum and Lumped-Mass Models for Hyper-Redundant Manipulator Mechanics

1993 ◽  
Author(s):  
Gregory S. Chirikjian
Keyword(s):  
Continuum Model ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Lumped Mass ◽  
Mass Model ◽  
Joint Torques ◽  
Lumped Mass Model ◽  
The Continuum

Abstract The most efficient methods for representing dynamics in the literature require serial computations which are proportional to the number of manipulator degrees-of-freedom. Furthermore, these methods are not fully parallelizable. For ‘hyper-redundant’ manipulators, which may have tens, hundreds, or thousands of actuators, these formulations preclude real time implementation. This paper therefore looks at the mechanics of hyper-redundant manipulators from the point of view of an approximation to an ‘infinite degree-of-freedom’ (or continuum) problem. The dynamics for this infinite dimensional case is developed. The approximate dynamics of actual hyper-redundant manipulators is then reduced to a problem which is O(1) in the number of serial computations, i.e., the algorithm is O(n) in the total number of computations, but these computations are completely parallelizable. This is achieved by ‘projecting’ the dynamics of the continuum model onto the actual robotic structure. The results are compared with a lumped mass model of a particular hyper-redundant manipulator. It is found that the continuum model can be used to generate joint torques to within ten percent of values computed from the lumped mass model.

scholarly journals A Solution of the Inverse Kinematics Problem for a 7-Degrees-of-Freedom Serial Redundant Manipulator Using Gröbner Bases Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Sérgio Ricardo Xavier da Silva ◽  
Leizer Schnitman ◽  
Vitalino Cesca Filho
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Operational Performance ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
All Solutions ◽  
Inverse Kinematics Problem ◽  
Algebraic Computing

This article presents a solution of the inverse kinematics problem of 7-degrees-of-freedom serial redundant manipulators. A 7-degrees-of-freedom (7-DoF) redundant manipulator can avoid obstacles and thus improve operational performance. However, its inverse kinematics is difficult to solve since it has one more DoF than that necessary for reaching the whole workspace, which causes infinite solutions. In this article, Gröbner bases theory is proposed to solve the inverse kinematics. First, the Denavit–Hartenberg model for the manipulator is established. Second, different joint configurations are obtained using Gröbner bases theory. All solutions are confirmed with the aid of algebraic computing software, confirming that this method is accurate and easy to be implemented.

scholarly journals Obstacle avoidance and multitarget tracking of a super redundant modular manipulator based on Bezier curve and particle swarm optimization

2020 ◽  
Author(s):  
chen li ◽  
Ying Ma ◽  
Yu Zhang ◽  
Jinguo Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Obstacle Avoidance ◽  
Trajectory Tracking ◽  
Degrees Of Freedom ◽  
Optimization Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Redundant Manipulator ◽  
Swarm Optimization ◽  
Integrated Optimization

Abstract A super redundant serpentine manipulator has slender structure and multiple degrees of freedom. It can travel through narrow spaces and move in complex spaces. This manipulator is composed of many modules that can form different lengths of robot arms for different application sites. The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space. This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator. In this integrated optimization, path planning is established on a Bezier curve, and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator. A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy. The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve. Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints. The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.

scholarly journals Obstacle Avoidance and Multitarget Tracking of a Super Redundant Modular Manipulator Based on Bezier Curve and Particle Swarm Optimization

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Li Chen ◽  
Ying Ma ◽  
Yu Zhang ◽  
Jinguo Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Obstacle Avoidance ◽  
Trajectory Tracking ◽  
Degrees Of Freedom ◽  
Optimization Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Redundant Manipulator ◽  
Swarm Optimization ◽  
Integrated Optimization

Abstract A super redundant serpentine manipulator has slender structure and multiple degrees of freedom. It can travel through narrow spaces and move in complex spaces. This manipulator is composed of many modules that can form different lengths of robot arms for different application sites. The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space. This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator. In this integrated optimization, path planning is established on a Bezier curve, and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator. A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy. The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve. Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints. The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.

scholarly journals A trajectory planning method for the redundant manipulator based on configuration plane

2021 ◽  
Vol 18 (6) ◽  
pp. 172988142110585
Author(s):  
Yanhui Wei ◽  
Zhi Zheng ◽  
Qiangqiang Li ◽  
Jialin He
Keyword(s):  
Velocity Distribution ◽  
Obstacle Avoidance ◽  
Trajectory Planning ◽  
Spatial Interpolation ◽  
Planning Method ◽  
Redundant Manipulators ◽  
Analysis Method ◽  
Kinematics Analysis ◽  
Redundant Manipulator

This study focuses on the method of trajectory planning of spatial obstacle avoidance for redundant manipulators based on configuration plane method. Firstly, according to the summary of the work configuration for redundant manipulator, kinematics analysis method based on configuration plane is proposed, which helps to establish a basic kinematics model of configuration plane. Secondly, the analysis of velocity is conducted and velocity iterative formula is derived. Then, the process of the trajectory planning for redundant manipulator based on the velocity distribution of configuration plane is given, during which some key procedures such as the determination of work configuration, achieving spatial obstacle avoidance, and analysis of velocity distribution are deduced. Finally, the simulation of spatial circle trajectory planning for the 7-degree-of-freedom redundant manipulator is done. The experimental results show that the proposed trajectory planning method for redundant manipulator can satisfy the requirements of complex spatial obstacle avoidance and increase the controllability of the trajectory between spatial interpolation points of the manipulator’s end effector.

scholarly journals A geometric approach for follow-the-leader motion of serpentine manipulator

2019 ◽  
Vol 16 (5) ◽  
pp. 172988141987463 ◽  
Author(s):  
Haibo Xie ◽  
Cheng Wang ◽  
Shusen Li ◽  
Liang Hu ◽  
Huayong Yang
Keyword(s):  
Path Planning ◽  
Real Time ◽  
Obstacle Avoidance ◽  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Computation Time ◽  
Geometric Approach ◽  
Real Time Control ◽  
Time Control ◽  
The Ideal

This article presents a geometric approach for path planning of serpentine manipulator for real-time control in confined spaces. Firstly, the mechanical design of a serpentine manipulator is introduced, and its kinematics is analyzed. As the serpentine manipulator usually has more than 10 degrees of freedom, the motion control and obstacle avoidance are difficult considering its inverse kinematics. Follow-the-leader is an ideal path planning method for serpentine manipulator, as the manipulator moves forward, all the sections follow the path that the tip of manipulator has passed, which simplifies the obstacle avoidance. The realization of follow-the-leader method is to find the new configurations of the manipulator that can fit the ideal path with small errors. In this article, a novel geometric approach for follow-the-leader motion is proposed to solve new configurations with high precision of location and less computation time. The method is validated through simulation and the deviation from the ideal path is analyzed, simulation results show that calculation time for per step is less than 0.5 ms for a serpentine manipulator with 10 sections. To verify the follow-the-leader method, a 13-degree-of-freedom serpentine manipulator system with 6 sections was built, and 12 magnetic rotary encoders were embedded into the universal joints to collect data of rotation angles of each section. Experimental results show that the manipulator can carry out follow-the-leader motion as expected in real time.

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