Singularity Avoidance of Task-Redundant Robots in Pointing Tasks: On Nullspace Projection and Cardan Angles as Orientation Coordinates

Robot manipulators are often deployed in tool-symmetric tasks, which only requires defining end effector position and pointing direction. In this case six-axis serial industrial robots and full-mobility (spatial) parallel robots have one degree of task redundancy. Using Cardan angles as orientation coordinates, a unified formulation of the position-level and second-order inverse kinematics problem is set up for both robot types. An efficient scheme for difference-quotient approximation of gradients of performance criteria for projection into the task redundancy's nullspace is presented. The simulation example of a hexapod robot shows that avoiding and exiting parallel robot singularities of type II is possible with the nullspace of all joints. The nullspace controller scheme can be used in offline trajectory optimization and in online motion generation

Modeling parallel robot kinematics for 3T2R and 3T3R tasks using reciprocal sets of Euler angles

Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom ("3T2R"). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection

Exploiting Dynamics Parameter Linearity for Design Optimization in Combined Structural and Dimensional Robot Synthesis

In the design optimization of robot manipulators regarding drive train and link geometries the dynamics equations have to be evaluated repeatedly. The method proposed in this paper reduces the computational effort in the dynamics evaluations by using the property of parameter linearity of the dynamics equations. The combined structural and dimensional synthesis of robot manipulators is adapted in a set of hierarchical optimization loops to exploit this dynamics property. By this means a reduction of computation time for the inverse dynamics in the synthesis of up to factor three is possible

Towards Human-Robot Collaboration with Parallel Robots by Kinetostatic Analysis, Impedance Control and Contact Detection

Parallel robots provide the potential to be lever-aged for human-robot collaboration (HRC) due to low collision energies even at high speeds resulting from their reduced moving masses. However, the risk of unintended contact with the leg chains increases compared to the structure of serial robots. As a first step towards HRC, contact cases on the whole parallel robot structure are investigated and a disturbance observer based on generalized momenta and measurements of motor current is applied. In addition, a Kalman filter and a second-order sliding-mode observer based on generalized momenta are compared in terms of error and detection time. Gearless direct drives with low friction improve external force estimation and enable low impedance. The experimental validation is performed with two force-torque sensors and a kinetostatic model. This allows a new identification method of the motor torque constant of an assembled parallel robot to estimate external forces from the motor current and via a dynamics model. A Cartesian impedance control scheme for compliant robot-environmental dynamics with stiffness from 0.1-2N/mm and the force observation for low forces over the entire structure are validated. The observers are used for collisions and clamping at velocities of 0.4-0.9 m/s for detection within 9–58 ms and a reaction in the form of a zero-g mode.© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Resolution of Functional Redundancy for 3T2R Robot Tasks using Two Sets of Reciprocal Euler Angles

Robotic tasks like welding or drilling with three translational and only two rotational degrees of freedom ("3T2R") are of high industrial relevance but are rather scarcely addressed in scientific publications. Existing solutions for the resolution of the functional redundancy of robotic manipulators with more than five axes performing these tasks either expand the full kinematic formulation or reduce it in intermediate steps. This paper presents an approach to reduce the kinematic formulation from the start to solve the problem in a simpler way. This is done by using a set of reciprocal Euler angles to describe the end-effector orientation and the orientation error in inverse kinematics

Auto-tuning of PID Controllers for Robotic Manipulators Using PSO and MOPSO

This work proposes two approaches to automatic tuning of PID position controllers based on different global optimization strategies. The chosen optimization algorithms are PSO and MOPSO, i. e. the problem is handled as a single objective problem in the first implementation and as a multiobjective problem in the second one. The auto-tuning is performed without assuming any previous knowledge of the robot dynamics. The objective functions are evaluated depending on real movements of the robot. Therefore, constraints guaranteeing safe and stable robot motion are necessary, namely: a maximum joint torque constraint, a maximum position error constraint and an oscillation constraint. Because of the practical nature of the problem in hand, constraints must be observed online. This requires adaptation of the optimization algorithm for reliable observance of the constraints without affecting the convergence rate of the objective function. Finally, Experimental results of a 3-DOF robot for different trajectories and with different settings show the validity of the two approaches and demonstrate the advantages and disadvantages of every method

A Practical Approach for the Auto-tuning of PD Controllers for Robotic Manipulators using Particle Swarm Optimization

An auto-tuning method of PD controllers for robotic manipulators is proposed. This method suggests a practical implementation of the particle swarm optimization technique in order to find optimal gain values achieving the best tracking of a predefined position trajectory. For this purpose, The integral of the absolute error IAE is used as a cost function for the optimization algorithm. The optimization is achieved by performing the desired movement of the robot iteratively and evaluating the cost function for every iteration. Therefor, the necessary constraints that guarantee a safe and stable movement of the robot are defined, which are: a maximum joint torque constraint, a maximum position error constraint and an oscillation constraint. A constraint handling approach is suggested for the optimization algorithm in order to adapt it to the problem in hand. Finally, the efficiency of the proposed method is verified through a practical experiment on a real robot