A contribution to minimum-time task-space path-following problem for redundant manipulators

The minimum-time path-following problem for non-redundant manipulator has already been analyzed and a number of efficient solution algorithms have been proposed. These algorithms can be applied also to redundant manipulators if the path is assigned in the joint space. If the path is assigned in the task space instead, how to exploit kinematic redundancy to reduce the execution time is still an open problem. In this paper it is proposed to follow a heuristic approach to choose between different solutions to the inverse kinematics problem that underlies the minimum-time path-following control problem. The aim is to obtain a joint-space path which configures the manipulator so as to improve acceleration/deceleration capabilities of the end-effector. This is obtained by penalizing the motion of joints with higher inertia-to-torque ratios. Numerical results are presented for an “easy-to-understand” three degree-of-freedom planar manipulator involved in two-dimensional paths.

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Improving minimum-time task-space path-following algorithms for redundant manipulators

Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104) ◽

10.1109/cca.1998.728538 ◽

2002 ◽

Author(s):

P. Chiacchio ◽

M. Concilio

Keyword(s):

Path Following ◽

Minimum Time ◽

Redundant Manipulators ◽

Task Space ◽

Time Task ◽

Path Following Algorithms

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Computing Robust Inverse Kinematics Under Uncertainty

Volume 5A: 43rd Mechanisms and Robotics Conference ◽

10.1115/detc2019-97945 ◽

2019 ◽

Author(s):

Anirban Sinha ◽

Nilanjan Chakraborty

Keyword(s):

Inverse Kinematics ◽

Joint Space ◽

Redundant Manipulators ◽

Task Space ◽

Success Rates ◽

Redundant Manipulator ◽

Space Error ◽

Inverse Kinematics Problem ◽

Robotic Tasks ◽

Present Simulation

Abstract Robotic tasks, like reaching a pre-grasp configuration, are specified in the end effector space or task space, whereas, robot motion is controlled in joint space. Because of inherent actuation errors in joint space, robots cannot achieve desired configurations in task space exactly. Furthermore, different inverse kinematics (IK) solutions map joint space error set to task space differently. Thus for a given task with a prescribed error tolerance, all IK solutions will not be guaranteed to successfully execute the task. Any IK solution that is guaranteed to execute a task (possibly with high probability) irrespective of the realization of the joint space error is called a robust IK solution. In this paper we formulate and solve the robust inverse kinematics problem for redundant manipulators with actuation uncertainties (errors). We also present simulation and experimental results on a 7-DoF redundant manipulator for two applications, namely, a pre-grasp positioning and a pre-insertion positioning scenario. Our results show that the robust IK solutions result in higher success rates and also allows the robot to self-evaluate how successful it might be in any application scenario.

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Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Robotica ◽

10.1017/s0263574708004384 ◽

2008 ◽

Vol 26 (6) ◽

pp. 791-802 ◽

Cited By ~ 22

Author(s):

Flavio Firmani ◽

Alp Zibil ◽

Scott B. Nokleby ◽

Ron P. Podhorodeski

Keyword(s):

Parallel Manipulators ◽

Joint Space ◽

Linear Mapping ◽

Redundant Manipulators ◽

Task Space ◽

Performance Indices ◽

Study Case ◽

And Performance ◽

Planar Parallel Manipulators

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

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Robust Finite Time Path Following Control for Underactuated Ships with Ship-to-Ship Avoidance Strategy

2019 Chinese Control Conference (CCC) ◽

10.23919/chicc.2019.8865501 ◽

2019 ◽

Author(s):

Zhang Guoqing ◽

Zhang Chenliang ◽

Zhang Xianku ◽

Zhang Weidong

Keyword(s):

Finite Time ◽

Path Following ◽

Time Path ◽

Path Following Control ◽

Avoidance Strategy

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Finite-Time Path Following Control of an Underactuated Marine Surface Vessel with Input and Output Constraints

Applied Sciences ◽

10.3390/app10186447 ◽

2020 ◽

Vol 10 (18) ◽

pp. 6447

Author(s):

Mingyu Fu ◽

Lulu Wang

Keyword(s):

Finite Time ◽

Input Saturation ◽

Path Following ◽

Parametric Uncertainties ◽

External Disturbances ◽

Time Path ◽

Path Following Control ◽

Control Scheme ◽

Marine Surface ◽

Surface Vessel

This paper develops a finite-time path following control scheme for an underactuated marine surface vessel (MSV) with external disturbances, model parametric uncertainties, position constraint and input saturation. Initially, based on the time-varying barrier Lyapunov function (BLF), the finite-time line-of-sight (FT-LOS) guidance law is proposed to obtain the desired yaw angle and simultaneously constrain the position error of the underactuated MSV. Furthermore, the finite-time path following constraint controllers are designed to achieve tracking control in finite time. Additionally, considering the model parametric uncertainties and external disturbances, the finite-time disturbance observers are proposed to estimate the compound disturbance. For the sake of avoiding the input saturation and satisfying the requirements of finite-time convergence, the finite-time input saturation compensators were designed. The stability analysis shows that the proposed finite-time path following control scheme can strictly guarantee the constraint requirements of the position, and all error signals of the whole control system can converge into a small neighborhood around zero in finite time. Finally, comparative simulation results show the effectiveness and superiority of the proposed finite-time path following control scheme.

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A sampling-based optimized algorithm for task-constrained motion planning

International Journal of Advanced Robotic Systems ◽

10.1177/1729881419847378 ◽

2019 ◽

Vol 16 (3) ◽

pp. 172988141984737 ◽

Cited By ~ 1

Author(s):

Kai Mi ◽

Haojian Zhang ◽

Jun Zheng ◽

Jianhua Hu ◽

Dengxiang Zhuang ◽

...

Keyword(s):

Motion Planning ◽

Sampling Methods ◽

Tracking Error ◽

Joint Space ◽

Planning Problem ◽

Redundant Manipulators ◽

Task Space ◽

Constrained Motion ◽

Smooth Path ◽

Planning Algorithm

We consider a motion planning problem with task space constraints in a complex environment for redundant manipulators. For this problem, we propose a motion planning algorithm that combines kinematics control with rapidly exploring random sampling methods. Meanwhile, we introduce an optimization structure similar to dynamic programming into the algorithm. The proposed algorithm can generate an asymptotically optimized smooth path in joint space, which continuously satisfies task space constraints and avoids obstacles. We have confirmed that the proposed algorithm is probabilistically complete and asymptotically optimized. Finally, we conduct multiple experiments with path length and tracking error as optimization targets and the planning results reflect the optimization effect of the algorithm.

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