Dynamics of the Orthoglide parallel robot

Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other. Three identical legs connecting to the moving platform are located on three planes being perpendicular to each other too. Knowing the position and the translation motion of the platform, we develop the inverse kinematics problem and determine the position, velocity and acceleration of each element of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the input forces and the powers of the three actuators

Efficient dynamic simulation for multiple chain robotic mechanisms

An efficient O(mN) algorithm for dynamic simulation of simple closed-chain robotic mechanisms is presented, where m is the number of chains, and N is the number of degrees of freedom for each chain. It is based on computation of the operational space inertia matrix (6 x 6) for each chain as seen by the body, load, or object. Also, computation of the chain dynamics, when opened at one end, is required, and the most efficient algorithm is used for this purpose. Parallel implementation of the dynamics for each chain results in an O(N) + O(log sub 2 m+1) algorithm

Characterization of robotics parallel algorithms and mapping onto a reconfigurable SIMD machine

The kinematics, dynamics, Jacobian, and their corresponding inverse computations are six essential problems in the control of robot manipulators. Efficient parallel algorithms for these computations are discussed and analyzed. Their characteristics are identified and a scheme on the mapping of these algorithms to a reconfigurable parallel architecture is presented. Based on the characteristics including type of parallelism, degree of parallelism, uniformity of the operations, fundamental operations, data dependencies, and communication requirement, it is shown that most of the algorithms for robotic computations possess highly regular properties and some common structures, especially the linear recursive structure. Moreover, they are well-suited to be implemented on a single-instruction-stream multiple-data-stream (SIMD) computer with reconfigurable interconnection network. The model of a reconfigurable dual network SIMD machine with internal direct feedback is introduced. A systematic procedure internal direct feedback is introduced. A systematic procedure to map these computations to the proposed machine is presented. A new scheduling problem for SIMD machines is investigated and a heuristic algorithm, called neighborhood scheduling, that reorders the processing sequence of subtasks to reduce the communication time is described. Mapping results of a benchmark algorithm are illustrated and discussed

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied

Computer algebra for solving dynamics problems of piezoelectric robots with large number of joints

The application of general control theory to complex mechanical systems represents an extremely difficult problem. If industrial piezoelectric robots have large number of joints, development of new control algorithms is unavoidable in order to achieve high positioning accuracy. The efficiency of computer algebra application was compared with the most popular methods of forming the dynamic equations of robots in real time. To this end, a computer algebra system VIBRAN was used. Expressions for the generalized inertia matrix of the robots have been derived by means of the computer algebra technique with the following automatic program code generation. As shown in the paper, such application could drastically reduce the number of floating point product operations that are required for efficient numerical simulation of piezoelectric robots

A survey of adaptive control technology in robotics

Previous work on the adaptive control of robotic systems is reviewed. Although the field is relatively new and does not yet represent a mature discipline, considerable attention has been given to the design of sophisticated robot controllers. Here, adaptive control methods are divided into model reference adaptive systems and self-tuning regulators with further definition of various approaches given in each class. The similarity and distinct features of the designed controllers are delineated and tabulated to enhance comparative review

An Omnidirectional Aerial Manipulation Platform for Contact-Based Inspection

This paper presents an omnidirectional aerial manipulation platform for robust and responsive interaction with unstructured environments, toward the goal of contact-based inspection. The fully actuated tilt-rotor aerial system is equipped with a rigidly mounted end-effector, and is able to exert a 6 degree of freedom force and torque, decoupling the system's translational and rotational dynamics, and enabling precise interaction with the environment while maintaining stability. An impedance controller with selective apparent inertia is formulated to permit compliance in certain degrees of freedom while achieving precise trajectory tracking and disturbance rejection in others. Experiments demonstrate disturbance rejection, push-and-slide interaction, and on-board state estimation with depth servoing to interact with local surfaces. The system is also validated as a tool for contact-based non-destructive testing of concrete infrastructure.Comment: Accepted submission to Robotics: Science and Systems conference 2019. 9 pages, 12 figure

On the optimal design of parallel robots taking into account their deformations and natural frequencies

This paper discusses the utility of using simple stiffness and vibrations models, based on the Jacobian matrix of a manipulator and only the rigidity of the actuators, whenever its geometry is optimised. In many works, these simplified models are used to propose optimal design of robots. However, the elasticity of the drive system is often negligible in comparison with the elasticity of the elements, especially in applications where high dynamic performances are needed. Therefore, the use of such a simplified model may lead to the creation of robots with long legs, which will be submitted to large bending and twisting deformations. This paper presents an example of manipulator for which it is preferable to use a complete stiffness or vibration model to obtain the most suitable design and shows that the use of simplified models can lead to mechanisms with poorer rigidity

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements