Simplified Stable Admittance Control Using End-Effector Orientations
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ORIGINAL RESEARCH
Simplified Stable Admittance Control Using End-Effector Orientations Wen Yu1 · Adolfo Perrusquía1 Accepted: 17 July 2019 © Springer Nature B.V. 2019
Abstract Admittance control is used mainly for human–robot interaction. It transforms forces and torques to the desired position and orientation of the end effector. When the admittance control is in the task space, it needs the Jacobian matrix, while in the joint space, it requires the inverse kinematics. This paper modifies the admittance control using only the orientation components of the end-effector to avoid the calculation of the inverse kinematics and the Jacobian matrix. We use geometric properties, adaptive control and sliding mode control to approximate them. The stability of those controllers is proven. Experiments are presented in real time with a 2-DOF pan and tilt robot and a 4-DOF exoskeleton. The results of the experiment show the effectiveness of the proposed controllers. Keywords Admittance control · Stability · Sliding mode control
1 Introduction Human–robot cooperative control is an emerging field in robotics, which provides an interaction between human action and the robot [1]. The main objective of cooperative control is to generate specific tasks to combine human abilities and robot properties [2], for example, co-manipulation [3], haptic operation [4,5], learning from demonstrations [6]. Admittance control is one of the most common methods to make the connection between humans and robots [7]. The admittance control can be considered as a dynamic mapping of forces/torques to the movement (position or velocity). It uses forces/torques to admit a certain number of movements [8]. In general, the relationship between forces/torques and movement is imposed by a spring-mass damper system. The parameters of this system represent the robot’s ability to follow the path given by the human operator [1].
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Wen Yu [email protected] Departamento de Control Automático, CINVESTAV-IPN (National Polytechnic Institute), Av.IPN 2508, 07360 Mexico City, Mexico
Normal admittance control requires inverse kinematics in joint space,1 so that the movement of the robot is linearized and decoupled globally [8,9]. The main problem with inverse kinematics is that their solutions (if they exist) are coupled by the position of the end-effector and kinematic parameters. The output trajectories of the admittance model are practically decoupled, which causes singularity problems in the joint solutions. The trajectories generated from the admittance control are in task space.2 Although the inverse kinematics can be avoided, the output of the admittance model can not be applied to the robot joints. It requires the Jacobian to transform the control signals of the task space into the joint space [10]. The main problem of the Jacobian is that it depends on joint measures and kinematic parameters that are not always available, even more can make the closedloop system unstable, because it presents the same problem of inverse kinematics, i.e., the Jacobian i
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