Modeling Impedance Control with Limited Interaction Power for A 2R Planar Robot Arm

Impedance control is a widely used concept in robotics to regulate the interaction between a robot and its environment in tasks such as pushing, polishing, cleaning, and grinding. The impedance controller regulates the dynamic relationship between the robot and the environment. The force applied by the robot to the environment depends on the position of the robot arm endpoint and the corresponding impedance. The interaction force directly affects the energy consumed by the robot, impacting the torques in the joints. This fact makes it imperative to control the interaction between the robot and the environment. However, in certain scenarios, the interaction power of the robot may be limited due to constraints such as actuator saturation, limited energy supply, or safety concerns. In these situations, it becomes crucial to model impedance control with limited interaction power to achieve effective and safe robot behavior. This study presents a detailed analysis of impedance control with limited interaction power, with a focus on developing an analytical model that accurately captures the dynamic behavior of the system while considering constraints on interaction power. The proposed model provides a framework for designing control strategies that can achieve desired behavior while satisfying the limitations. To optimize the impedance controller parameters, the Bees Algorithm is used. Following the optimization process, a model for interaction power limitation was developed, resulting in limited interaction power consumption for each joint. The effectiveness of the proposed model is demonstrated through simulations, showing successful control of the interaction between the robot and its environment with limited interaction power. Numerical and graphical results of the study are presented.