Flat control of industrial robotic manipulators

Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols

A Relevant Reduction Method for Dynamic Modeling of a Seven-linked Humanoid Robot in the Three-dimensional Space

Dynamic modeling means deriving equations that explicitly describes the relationship between force and motion in a system. To be able to control a robot manipulator as required by its operation, it is important to consider the dynamic model in design of the control algorithm and simulation of motion. In general there are two approaches available; the Euler-Lagrange formulation and the Newton-Euler formulation. This thesis investigates the Lagrange-Euler method in detail. A complete derivation of the method is done using two degree of freedom serial manipulator with revolute joints in the presence and absence of gravitational force. The mathematical model for the Dynamic behaviour of the two degree of freedom manipulator is developed. The dynamic parameters of the system are estimated, and the validity of the resulting dynamic model is verified by several simulations, that describe the dynamic response of the manipulator to input actuator torques. A suggestion for future work is performing thorough dynamic parameter identification. An improved model can ultimately be implemented in the controller of the manipulator, and optimized for a specific job task. Keywords-Torque, Dynamics, manipulator, force, motion I-INTRODUCTION During working cycle a manipulator must accelerate, move at constant speed and decelerate. The time varying position and orientation of the manipulator is termed as its dynamic behaviour. Time varying torques is applied at the joints to balance out internal and external force. Dynamics is a huge field of study devoted to studying the forces required to cause motion [1], [2]. The dynamic motion of the manipulator arm in a robotic system is produced by the torques generated by the actuators. This relationship between the input torques and the time rates of change of the robot arm components configurations, represent the dynamic modeling of the robotic system which is concerned with the derivation of the equations of motion of the manipulator as a function of the forces and moments acting on. So, the dynamic modeling of a robot manipulator consists of finding the mapping between the forces exerted on the structures and the joint positions, velocities and accelerations [3]. A good model has to satisfy two conflicting objectives. It must include enough detail to represent the real behaviour of the robot with sufficient accuracy, and it should permit an efficient, stable evaluation not only of the model equations but also of their derivatives that are needed in optimization. The availability of the dynamic model is very useful for mechanical design of the structure, choice of actuators, determination of control strategies, and computer simulation manipulator motion. A robot manipulator is basically a positioning device. To control the position we must know the dynamic properties of the manipulator in order to know how much force to exert on it to cause it to move: too little force and the manipulator is slow to react; too much force and the arm may crash into objects or oscillate about its desired position. A significant amount of research has been reported concerning optimal trajectory planning using evolutionary methods for an industrial manipulator system. Research made the use of cubic spline curves to generate the trajectory between the intermediate points of the path. The problem of kinematics is solved for two-degree-of-freedom linear industrial manipulators. The Newton-Euler technique is used for the formulation of the dynamic equations of the manipulator. The effectiveness of the proposed method is verified through MATLAB simulations in [7], it has shown a trajectory generation for a two link robot manipulator without the use of the inverse Jacobian matrix, in which the cubic spline approach was employed. Robotic manipulators will play important roles in future space missions. The control of such space manipulators poses planning and control problems not found in terrestrial fixed-base manipulators due to the dynamic coupling between space manipulators and their spacecraft. A number of control techniques for such systems have been proposed; these schemes can be classified in three categories. In the first category, spacecraft position and attitude are controlled by reaction jets to compensate for any manipulator dynamic forces exerted on the spacecraft. In this case, control laws for earth-bound manipulators can be used, but the utility of such systems may be limited because manipulator motions can both saturate the reaction jet system and consume relatively large amounts of attitude control fuel, limiting the useful life of the system [10], [11], and [14]. In the second category, the spacecraft attitude is controlled, although not its translation, by using reaction wheels or attitude control jets [12]. The control of these systems is somewhat more complicated than that of the first category, although a technique called the Virtual Manipulator (VM) can be used to simplify the problem [10], [11], [12], [13], and [14]. The third proposed category assumes a free-floating system in order to conserve fuel or electrical power [10], [15], and [16]. Such a system permits the spacecraft to move freely in response to manipulator motions. These too can be modelled using the VM approach [15]. Work was done on control algorithm for free-floating space manipulators in [14]. It was shown that nearly and algorithm that can be applied to conventional International Journal of Engineering Research & Technology (IJERT) Vol. 1 Issue 5, July 2012 ISSN: 2278-0181

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The Dynamics of Fixed Base and Free-Floating Robotic Manipulator

Increasingly, robots have more degrees of freedom (DOF), imposing a need for calculating more complex dynamics. As a result, better efficiency in carrying out dynamics computations is becoming more important. In this study, an efficient method for computing the joint space inertia matrix (JSIM) for high DOF serially linked robots is addressed. We call this method the Geometric Dynamics Algorithm for High number of robot Joints (GDAHJ). GDAHJ is non-symbolic, preserve simple formulation, and it is convenient for numerical implementation. This is achieved by simplifying the way to recursively derive the mass-matrix exploiting the unique property of each column of the JSIM and minimizing the number of operations with $O(n^{2})$ complexity. Results compare favorably with existing methods, achieving better performance over state-of-the-art by Featherstone when applied for robots with more than 13 DOF.

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Reducing the Computational Complexity of Mass-Matrix Calculation for High DOF Robots

Dynamic modeling means deriving equations that explicitly describes the relationship between force and motion in a system. To be able to control a robot manipulator as required by its operation, it is important to consider the dynamic model in design of the control algorithm and simulation of motion. In general there are two approaches available; the Euler-Lagrange formulation and the Newton-Euler formulation. This thesis explains briefly the differences of the formulations, and then research the Newton-Euler method in detail. A complete derivation of the method is derived, and an automated framework for applying the method on any serial manipulator with revolute joints is presented. By using the framework, the Newton-Euler formulation is applied on a modern industrial manipulator with six degrees of freedom. The dynamic parameters of the system are estimated, and the validity of the resulting dynamic model is verified by several simulations in open and closed loop. The simulations show that the system is unstable in open loop, and that it achieves global asymptotic stability in closed loop with gravity compensation, by including PD controllers with independent joint control. The latter is a confirmation of a mathematical proof based on a Lyapunov stability analysis, which is presented as well. Equivalent simulations of the dynamic model of the same manipulator derived by the standard Euler-Lagrange formulation show that the efficiency of recursive procedures is way higher that treating the manipulator as a whole. A suggestion for future work is performing thorough dynamic parameter identification. An improved model can ultimately be implemented in the controller of the manipulator, and optimized for a specific job task.

Herman Høifødt

Papers

Dynamic Modeling and Simulation of Robot Manipulators: The Newton-Euler Formulation