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This study investigates the dynamics of planar open-loop robotic systems with n-link elastic arms connected via revolute joints, focusing on multiple collision phenomena. The equations of motion are derived using the recursive Gibbs-Appell algorithm, and collisioncontact dynamics are modeled with a regulated approach. Transverse vibrations of the links are modeled using the Timoshenko beam theory, incorporating structural damping and air resistance for improved accuracy. The joints are assumed to be frictionless and backlash-free, while friction forces are considered at ground contact points. The system operates in two phases: flight and collision. During collisions, viscoelastic forces introduce stiff differential equations, requiring special handling due to the short collision duration. Accurate detection of collision onset and termination is achieved using a novel computational algorithm. To validate the model, the dynamic behavior of a three-link robotic system is simulated. Four distinct mode shapes are used to analyze their effects on the elastic deformation of the links. A comparative analysis highlights the influence of mode shapes on system behavior, demonstrating the framework's precision and efficiency in modeling and simulation. [ABSTRACT FROM AUTHOR]

Featured Application: The article gives a detailed description on how to implement a custom force control for collaborative robots without knowing all the internal parameters. The methodology presented can be used in any manufacturing process capable of being carried out by a collaborative robot. Due to the elasticity of their joints, collaborative robots are seldom used in applications with force control. Besides, the industrial robot controllers are closed and do not allow the user to access the motor torques and other parameters, hindering the possibility of carrying out a customized control. A good alternative to achieve a custom force control is sending the output of the force regulator to the robot controller through motion commands (inner/outer loop control). There are different types of motion commands (e.g., position or velocity). They may be implemented in different ways (Jacobian inverse vs. Jacobian transpose), but this information is usually not available for the user. This article is dedicated to the analysis of the effect of different inner loops and their combination with several external controllers. Two of the most determinant factors found are the type of the inner loop and the stiffness matrix. The theoretical deductions have been experimentally verified on a collaborative robot UR3, allowing us to choose the best behaviour in a polishing operation according to pre-established criteria. [ABSTRACT FROM AUTHOR]

Due to the elasticity of their joints, collaborative robots are seldom used in applications with force control. Besides, the industrial robot controllers are closed and do not allow the user to access the motor torques and other parameters, hindering the possibility of carrying out a customized control. A good alternative to achieve a custom force control is sending the output of the force regulator to the robot controller through motion commands (inner/outer loop control). There are different types of motion commands (e.g., position or velocity). They may be implemented in different ways (Jacobian inverse vs. Jacobian transpose), but this information is usually not available for the user. This article is dedicated to the analysis of the effect of different inner loops and their combination with several external controllers. Two of the most determinant factors found are the type of the inner loop and the stiffness matrix. The theoretical deductions have been experimentally verified on a collaborative robot UR3, allowing us to choose the best behaviour in a polishing operation according to pre-established criteria.

The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinematic equation. To feed the neural network, experimental data were taken from an elastic robot arm for training the network, these data presented by joint angles, deformation variables and end-effector positions. The results of network training showed a good fit between the output results of the neural network and the targets data. In addition, this method for finding the inverse of kinematic equation proved its effectiveness and validation when applying the results of neural network practically in the robot’s operating software for controlling the real light robot’s position.

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