scholarly journals End-effector Cartesian stiffness shaping - sequential least squares programming approach

2021 ◽  
Vol 18 (1) ◽  
pp. 1-14
Author(s):  
Nikola Knezevic ◽  
Branko Lukic ◽  
Kosta Jovanovic ◽  
Leon Zlajpah ◽  
Tadej Petric
Keyword(s):  
Least Squares ◽  
Stiffness Matrix ◽  
Null Space ◽  
Joint Stiffness ◽  
Mechanical Impedance ◽  
Programming Algorithm ◽  
Programming Approach ◽  
Optimization Approach ◽  
End Effector ◽  
Cartesian Stiffness

Control of robot end-effector (EE) Cartesian stiffness matrix (or the whole mechanical impedance) is still a challenging open issue in physical humanrobot interaction (pHRI). This paper presents an optimization approach for shaping the robot EE Cartesian stiffness. This research targets collaborative robots with intrinsic compliance - serial elastic actuators (SEAs). Although robots with SEAs have constant joint stiffness, task redundancy (null-space) for a specific task could be used for robot reconfiguration and shaping the stiffness matrix while still keeping the EE position unchanged. The method proposed in this paper to investigate null-space reconfiguration's influence on Cartesian robot stiffness is based on the Sequential Least Squares Programming (SLSQP) algorithm, which presents an expansion of the quadratic programming algorithm for nonlinear functions with constraints. The method is tested in simulations for 4 DOF planar robot. Results are presented for control of the EE Cartesian stiffness initially along one axis, and then control of stiffness along both planar axis - shaping the main diagonal of the EE stiffness matrix.

scholarly journals Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Arthur Carlton-Jones ◽  
Elizabeth J. Paul ◽  
William Dorland
Keyword(s):  
Null Space ◽  
Radial Distance ◽  
Plasma Boundary ◽  
Optimization Approach ◽  
Surface Parameters ◽  
Fixed Boundary ◽  
Plasma Surface ◽  
Shape Gradient ◽  
Derivative Free ◽  
Boundary Optimization

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion, vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al., Nucl. Fusion, vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion, vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al., Nucl. Fusion, vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids, vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas, vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

scholarly journals Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study

PLoS ONE ◽  
2016 ◽  
Vol 11 (6) ◽  
pp. e0157010 ◽  
Author(s):  
Vincent Richard ◽  
Giuliano Lamberto ◽  
Tung-Wu Lu ◽  
Aurelio Cappozzo ◽  
Raphaël Dumas
Keyword(s):  
Knee Joint ◽  
Feasibility Study ◽  
Stiffness Matrix ◽  
Joint Stiffness ◽  
Knee Kinematics ◽  
Multi Body

scholarly journals Stiffness Modeling of Robotic-Manipulators Under Auxiliary Loadings

2012 ◽  
Author(s):  
Alexandr Klimchik ◽  
Anatol Pashkevich ◽  
Stéphane Caro ◽  
Damien Chablat
Keyword(s):  
Robotic Manipulators ◽  
Computationally Efficient ◽  
End Effector ◽  
Efficient Procedure ◽  
Stiffness Modeling ◽  
Cartesian Stiffness Matrix ◽  
Different Types ◽  
Mapping Equation ◽  
Linear Force ◽  
Cartesian Stiffness

The paper focuses on the extension of the virtual-joint-based stiffness modeling technique for the case of different types of loadings applied both to the robot end-effector and to manipulator intermediate points (auxiliary loading). It is assumed that the manipulator can be presented as a set of compliant links separated by passive or active joints. It proposes a computationally efficient procedure that is able to obtain a non-linear force-deflection relation taking into account the internal and external loadings. It also produces the Cartesian stiffness matrix. This allows to extend the classical stiffness mapping equation for the case of manipulators with auxiliary loading. The results are illustrated by numerical examples.

Robot Path Planning and Obstacle Avoidance: A Design Optimization Approach

1989 ◽  
Author(s):  
E. Sandgren ◽  
S. Venkataraman
Keyword(s):  
Path Planning ◽  
Design Optimization ◽  
Dynamic Programming Algorithm ◽  
Three Dimensional ◽  
Programming Algorithm ◽  
Optimization Approach ◽  
Robot Arm ◽  
Robot Path Planning ◽  
Real Time Control ◽  
Robot Path

Abstract A design optimization approach to robot path planning in a two dimensional workplace is presented. Obstacles are represented as a series of rectangular regions and collision detection is performed by an operation similar to clipping in computer graphics. The feasible design space is approximated by a discrete set of robot arm and gripper positions. Control is applied directly through the angular motion of each link. Feasible positions which are located between the initial and final robot link positions are grouped into stages. A dynamic programming algorithm is applied to locate the best state within each stage which minimizes the overall path length. An example is presented involving a three link planar manipulator. Extensions to three dimensional robot path planning and real time control in a dynamically changing workplace are discussed.

Cooperation and Null-Space Control of Networked Omni-Directional Mobile Manipulators

2020 ◽  
Author(s):  
Michael John Chua ◽  
Yen-Chen Liu
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Kinematic Model ◽  
Mobile Manipulator ◽  
Main Task ◽  
Mobile Manipulators ◽  
Robot Arm ◽  
Task Space ◽  
End Effector ◽  
Mobile Base

Abstract This paper presents cooperation and null-space control for networked mobile manipulators with high degrees of freedom (DOFs). First, kinematic model and Euler-Lagrange dynamic model of the mobile manipulator, which has an articulated robot arm mounted on a mobile base with omni-directional wheels, have been presented. Then, the dynamic decoupling has been considered so that the task-space and the null-space can be controlled separately to accomplish different missions. The motion of the end-effector is controlled in the task-space, and the force control is implemented to make sure the cooperation of the mobile manipulators, as well as the transportation tasks. Also, the null-space control for the manipulator has been combined into the decoupling control. For the mobile base, it is controlled in the null-space to track the velocity of the end-effector, avoid other agents, avoid the obstacles, and move in a defined range based on the length of the manipulator without affecting the main task. Numerical simulations have been addressed to demonstrate the proposed methods.

Analysis of Sparse Representation and Blind Source Separation

2004 ◽  
Vol 16 (6) ◽  
pp. 1193-1234 ◽  
Author(s):  
Yuanqing Li ◽  
Andrzej Cichocki ◽  
Shun-ichi Amari
Keyword(s):  
Sparse Representation ◽  
Blind Source Separation ◽  
Clustering Algorithm ◽  
Source Separation ◽  
Coefficient Matrix ◽  
Data Matrix ◽  
Programming Algorithm ◽  
Optimization Approach ◽  
Basis Matrix ◽  
Two Stage

In this letter, we analyze a two-stage cluster-then-l1-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l1—norm solution and the l0—norm solution is also analyzed according to a probabilistic framework. If the obtained l1—norm solution is sufficiently sparse, then it is equal to the l0—norm solution with a high probability. Furthermore, the l1—norm solution is robust to noise, but the l0—norm solution is not, showing that the l1—norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed

On-line multi-criteria based collision-free posture generation of redundant manipulator in constrained workspace

Robotica ◽  
2002 ◽  
Vol 20 (6) ◽  
pp. 625-636 ◽  
Author(s):  
Jin-Liang Chen ◽  
Jing-Sin Liu ◽  
Wan-Chi Lee ◽  
Tzu-Chen Liang
Keyword(s):  
Null Space ◽  
Large Degree ◽  
Redundancy Resolution ◽  
Secondary Tasks ◽  
End Effector ◽  
Robotic Arms ◽  
Tracking Motion ◽  
On Line ◽  
Joint Limits ◽  
Joint Velocity

The manipulator with a large degree of redundancy is useful for realizing multiple tasks such as maneuvering the robotic arms in the constrained workspace, e.g. the task of maneuvering the end-effector of the manipulator along a pre-specified path into a window. This paper presents an on-line technique based on a posture generation rule to compute a null-space joint velocity vector in a singularity-robust redundancy resolution method. This rule suggests that the end of each link has to track an implicit trajectory that is indirectly resulted from the constraint imposed on tracking motion of the end-effector. A proper posture can be determined by sequentially optimizing an objective function integrating multiple criteria of the orientation of each link from the end-effector toward the base link as the secondary task for redundancy resolution, by assuming one end of the link is clamped. The criteria flexibly incorporate obstacle avoidance, joint limits, preference of posture in tracking, and connection of posture to realize a compromise between the primary and secondary tasks. Furthermore, computational demanding of the posture is reduced due to the sequential link-by-link computation feature. Simulations show the effectiveness and flexibility of the proposed method in generating proper postures for the collision avoidance and the joint limits as a singularity-robust null-space projection vector in maneuvering redundant robots within constrained workspaces.

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