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.

Obstacle avoidance control for redundant manipulators using collidability measure

Robotica ◽  
2000 ◽  
Vol 18 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Su Il Choi ◽  
Byung Kook Kim
Keyword(s):  
Obstacle Avoidance ◽  
Control Algorithm ◽  
Null Space ◽  
Control Law ◽  
Redundant Manipulators ◽  
Redundancy Resolution ◽  
End Effector ◽  
Joint Torques ◽  
Avoidance Control ◽  
Joint Acceleration

We present an efficient obstacle avoidance control algorithm for redundant manipulators using a new measure called collidability measure. Considering moving directions of manipulator links, the collidability measure is defined as the sum of inverse of predicted collision distances between links and obstacles: This measure is suitable for obstacle avoidance since directions of moving links are as important as distances to obstacles. For kinematic or dynamic redundancy resolution, null space control is utilized to avoid obstacles by minimizing the collidability measure: We present a velocity-bounded kinematic control law which allows reasonably large gains to improve the system performance. Also, by clarifying decomposition in the joint acceleration level, we present a simple dynamic control law with bounded joint torques which guarantees tracking of a given end-effector trajectory and improves a kinematic cost function such as collidability measure. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.

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.

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.

Experimental Evaluation of a Criteria-Based Obstacle Avoidance Scheme

1999 ◽  
Author(s):  
Troy Harden ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Obstacle Avoidance ◽  
Experimental Evaluation ◽  
Null Space ◽  
Redundant Manipulators ◽  
Complex Environments ◽  
Software Library ◽  
Cluttered Environments ◽  
Collision Prevention ◽  
Dual Arm ◽  
Multiple Manipulators

Abstract Obstacle avoidance allows manipulators to work in cluttered environments without damaging themselves or their environment. It generally involves collision prevention and configuration optimization to avoid obstacles, with collision prevention being the only choice for non-redundant manipulators. In the case of redundant manipulators, one obstacle avoidance scheme uses null-space options for a given end-effector location, and subsequent ranking of these options to select the ‘best’ one based on input criteria. Under this scheme, four obstacle avoidance criteria have been developed. These four (and other non-obstacle avoidance) criteria along with workspace modeling have been implemented as an extension of the OSCAR C++ software library. This library can be used to develop obstacle avoidance applications involving multiple manipulators operating in complex environments. Experimental evaluation of this scheme is conducted on a 17 degree of freedom dual-arm robotic manipulator, and results are presented.

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.

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