Effective secondary task execution of redundant manipulators

Robotica ◽  
1998 ◽  
Vol 16 (4) ◽  
pp. 457-462 ◽  
Author(s):  
Jadran Lenarčič
Keyword(s):  
Projection Operator ◽  
Secondary Task ◽  
Numerical Experiments ◽  
Null Space ◽  
Numerical Procedure ◽  
Redundant Manipulators ◽  
Space Operator ◽  
Task Execution ◽  
Weighting Matrix ◽  
Space Projection

In standard pseudoinverse-based approaches to treat redundant manipulators, the vector of joint increments that corresponds to a desired motion in the space of the secondary task is projected in the Jacobian null space associated with the primary task. In general, this projection may distort the projected vector, so that the secondary task may not adequately be executed. A usual remedy is to rotate the null space projection operator by using a special-purpose weighting matrix. The problem, however, is that this rotation cannot be enforced arbitrarily since it influences the manipulator's performance. In our work we propose an algorithm that is independent on the chosen null space operator and always provides the best attainable motion in the space of the secondary task. Hence, the secondary task is executed more efficiently and the numerical procedure is more robust. A series of numerical experiments confirmed these results.

Obstacle avoidance for kinematically redundant manipulators using polyhedral approximations

2003 ◽  
Vol 217 (5) ◽  
pp. 533-542 ◽  
Author(s):  
X Zhu ◽  
H Qiao
Keyword(s):  
Obstacle Avoidance ◽  
Null Space ◽  
Convex Polyhedra ◽  
Redundant Manipulators ◽  
Essential Requirement ◽  
Joint Configuration ◽  
Projection Scheme ◽  
Almost Everywhere ◽  
Space Projection ◽  
Polyhedral Approximations

Collision avoidance is an essential requirement for a manipulator to complete a task in an environment with obstacles. In this paper, a pseudo-distance function is presented for a pair of convex polyhedra, along with the algorithm for calculating its derivative. On this basis, a potential field-based approach for obstacle avoidance of kinematically redundant manipulators is developed, with the manipulator links and the environmental obstacles being geometrically modelled as a set of convex polyhedra. The potential function is differentiable almost everywhere with respect to the joint configuration variables of the manipulator. It is incorporated in the ‘null space projection scheme’ in order to achieve obstacle avoidance. Simulation examples are presented to show the effectiveness of the proposed method.

scholarly journals Numerical Quantification of Controllability in the Null Space for Redundant Manipulators

2021 ◽  
Vol 11 (13) ◽  
pp. 6190
Author(s):  
Seonwoo Kim ◽  
Seongseop Yun ◽  
Dongjun Shin
Keyword(s):  
Root Mean Square ◽  
Null Space ◽  
Robotic Manipulators ◽  
Robotic Arm ◽  
Redundant Manipulators ◽  
Mean Square ◽  
Wide Range ◽  
Sinusoidal Input ◽  
Space Projection ◽  
Rms Error

Redundant motion, which is possible when robotic manipulators are over-actuated, can be used to control robot arms for a wide range of tasks. One of the best known methods for controlling redundancy is the null space projection, which assigns a priority while executing desired tasks. However, when the manipulator is projected into null space, its motion would be limited, since the motion is only permitted in the direction that does not interfere with the primary task. In this study, we have analyzed the null space projector matrix to derive the appropriate direction of the redundant motion by quantifying the allowed motion in each direction. As a result, we have found an ellipsoidal boundary, in which the redundant motion is permitted to move. We have named this ellipsoidal boundary as ’null space quality’ in directions. The proposed null space quality shows similar aspects with that of the robot manipulability, but it reveals a decisively different value when the manipulator operates within the null space. The experimental results showed that the robotic manipulator tracked the sinusoidal input trajectory with reduced root mean square (RMS) error by 33.84%. Furthermore, we have demonstrated the obstacle avoidance of a robotic arm utilizing the null space projector while considering the null space quality.

scholarly journals An Enhanced Smoothed L0-Norm Direction of Arrival Estimation Method Using Covariance Matrix

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4403
Author(s):  
Ji Woong Paik ◽  
Joon-Ho Lee ◽  
Wooyoung Hong
Keyword(s):  
Covariance Matrix ◽  
Phased Array ◽  
Null Space ◽  
Estimation Method ◽  
Direction Of Arrival ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Direction Of Arrival Estimation ◽  
Improve Performance ◽  
Space Projection

An enhanced smoothed l0-norm algorithm for the passive phased array system, which uses the covariance matrix of the received signal, is proposed in this paper. The SL0 (smoothed l0-norm) algorithm is a fast compressive-sensing-based DOA (direction-of-arrival) estimation algorithm that uses a single snapshot from the received signal. In the conventional SL0 algorithm, there are limitations in the resolution and the DOA estimation performance, since a single sample is used. If multiple snapshots are used, the conventional SL0 algorithm can improve performance in terms of the DOA estimation. In this paper, a covariance-fitting-based SL0 algorithm is proposed to further reduce the number of optimization variables when using multiple snapshots of the received signal. A cost function and a new null-space projection term of the sparse recovery for the proposed scheme are presented. In order to verify the performance of the proposed algorithm, we present the simulation results and the experimental results based on the measured data.

Learning a projection operator onto the null space of a linear imaging operator

2021 ◽  
Author(s):  
Joseph Kuo ◽  
Jason L. Granstedt ◽  
Umberto Villa ◽  
Mark A. Anastasio
Keyword(s):  
Projection Operator ◽  
Null Space

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

A Multi-Priority Control of Asymmetric Coordination for Redundant Dual-Arm Robot

2019 ◽  
Vol 16 (02) ◽  
pp. 1950008
Author(s):  
Fuhai Zhang ◽  
Jiadi Qu ◽  
He Liu ◽  
Yili Fu
Keyword(s):  
Secondary Task ◽  
Control Method ◽  
Null Space ◽  
Main Task ◽  
External Impact ◽  
Dual Arm Robot ◽  
End Effectors ◽  
Dual Arm ◽  
Arm Coordination ◽  
Asymmetric Coordination

The paper develops a multi-priority control method of asymmetric coordination for a redundant dual-arm robot. A novel dual-arm coordination impedance is introduced to the multi-priority control, and then the performance of the object tracking and the redundant joints is improved by the regulation of the relative Cartesian errors between two arms. The control of asymmetric coordination is divided into the main task and the secondary task. The control of the main task can regulate the two end-effectors’ errors and the relative errors by building the model of spatial parallel spring and damping (SPSDM), which establishes the dual-arm coordination impedance relation in Cartesian space. The control of the secondary task optimizes the performance of the redundant joint impedance and joint limit avoidance in null space. Finally, a typical asymmetric coordination experiment of peg-in-hole is carried out to verify the validity and feasibility of the proposed method. The results indicate that the proposed dual-arm coordination impedance can regulate the relative tracking errors between two objects directly, and in the context of the external impact force applied to the two end-effectors, the peg-in-hole dual-arm task can be achieved successfully.

scholarly journals A Synthetic Algorithm for Tracking a Moving Object in a Multiple-Dynamic Obstacles Environment Based on Kinematically Planar Redundant Manipulators

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Hongzhe Jin ◽  
Hui Zhang ◽  
Zhangxing Liu ◽  
Decai Yang ◽  
Dongyang Bie ◽  
...  
Keyword(s):  
Real Time ◽  
Null Space ◽  
Inverse Kinematic ◽  
Moving Object ◽  
Redundant Manipulators ◽  
Joint Angles ◽  
The Real ◽  
Time Path ◽  
Planar Manipulators ◽  
Spline Filter

This paper presents a synthetic algorithm for tracking a moving object in a multiple-dynamic obstacles environment based on kinematically planar manipulators. By observing the motions of the object and obstacles, Spline filter associated with polynomial fitting is utilized to predict their moving paths for a period of time in the future. Several feasible paths for the manipulator in Cartesian space can be planned according to the predicted moving paths and the defined feasibility criterion. The shortest one among these feasible paths is selected as the optimized path. Then the real-time path along the optimized path is planned for the manipulator to track the moving object in real-time. To improve the convergence rate of tracking, a virtual controller based on PD controller is designed to adaptively adjust the real-time path. In the process of tracking, the null space of inverse kinematic and the local rotation coordinate method (LRCM) are utilized for the arms and the end-effector to avoid obstacles, respectively. Finally, the moving object in a multiple-dynamic obstacles environment is thus tracked via real-time updating the joint angles of manipulator according to the iterative method. Simulation results show that the proposed algorithm is feasible to track a moving object in a multiple-dynamic obstacles environment.

MODELING EXPERIMENTAL DATA WITH POLYNOMIALS CHAOS

2018 ◽  
Vol 34 (1) ◽  
pp. 14-26
Author(s):  
Emeline Gayrard ◽  
Cédric Chauvière ◽  
Hacène Djellout ◽  
Pierre Bonnet
Keyword(s):  
Experimental Data ◽  
Constrained Optimization ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Polynomial Chaos ◽  
Numerical Procedure ◽  
Chaos Expansion ◽  
Constrained Optimization Problem ◽  
Raw Data ◽  
Accurate Representation

Given a raw data sample, the purpose of this paper is to design a numerical procedure to model this sample under the form of polynomial chaos expansion. The coefficients of the polynomial are computed as the solution to a constrained optimization problem. The procedure is first validated on samples coming from a known distribution and it is then applied to raw experimental data of unknown distribution. Numerical experiments show that only five coefficients of the Chaos expansions are required to get an accurate representation of a sample.

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