Abstract
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.
Highlights
Robot manipulators, which generally consist of six degrees of freedom (DoF), are widely adopted in industrial fields [1]
Redundancy is a crucial feature of robotic manipulators that can be utilized to execute a wide range of tasks with flexibility, dexterity, and versatility
In order to address this issue, we propose a new indicator named ’null space quality’, which evaluates the manipulability of a robot with null space projection
Summary
Robot manipulators, which generally consist of six degrees of freedom (DoF), are widely adopted in industrial fields [1]. Redundancy is a crucial feature of robotic manipulators that can be utilized to execute a wide range of tasks with flexibility, dexterity, and versatility Due to these unique characteristics, redundant manipulators can execute several tasks simultaneously with null space projection [2,3,4]. A new indicator that deals with this type of singularity is required to evaluate the controllability of a robot within the null space. It is not possible to evaluate the manipulability in its standard form when the null space projection is used due to the priority of the tasks This is because the movable direction of motion of a robot changes with the null space projector, in contrast to the movable direction of motion of a robot that considers every single joint. When the null space projection method is used, it is crucial to consider the controllable direction of a robot. The simulation and experiments were performed along the path of the infinitely possible solutions
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