Algorithme parallele et serie pour la simulation temps reel et la commande des robots manipulateurs.

Abstract

The work defined for this thesis concerns the study and analysis of serial cooperative robot manipulators to carry out tasks that cannot be performed by a single robot manipulator . The work also relates to the study , the selection and application of certain serial and parallel algorithms to speed up the calculations for simulation purposes and especially for real-time cooperative robot control and coordination. As there is no general model of cooperation, it is necessary first to contribute by developing and adapting geometric, kinematic and dynamic models appropriate for the case of cooperation, taking into account the constraints of the inter- The work defined for this thesis concerns the study and analysis of serial cooperative robot manipulators to carry out tasks that cannot be performed by a single robot manipulator . The work also relates to the study , the selection and application of certain serial and parallel algorithms to speed up the calculations for simulation purposes and especially for real-time cooperative robot control and coordination. As there is no general model of cooperation, it is necessary first to contribute by developing and adapting geometric, kinematic and dynamic models appropriate for the case of cooperation, taking into account the constraints of the inter- action of robots with the object to manipulate in its environment . A major constraint appears here because of the computation time becomes prohibitive and does not allow for real-time control of a cooperative group of robots. This is why , in the second place , it is necessary to contribute in exploring and implementing serial and parallel computing approaches. But also to accelerate the computation time for simulation and applications requiring control and real time coordination. This can be done by implementing parallel computing algorithms dedicated to network of processors as currently permitted by the transputer technology and DSP (Digital Signal Processing), clusters and supercomputers. Restricted to cases of serial robot manipula- tors in cooperation , an analysis of the state of the art as well as the results of our research has highlighted the following elements : a) - In terms of dynamic modeling , although the models of Newton - Lagrange and Newton-Euler have been developed for serial systems in open-chains , they are adaptable and generalized for cooperating robot manipulators systems . However, if the number of robots exceeds 3 robots of 6 DOF each, the mathematical formalism is difficult to organize and exploit because of the big size of symbolic expressions for the equations of the model. b ) - For the control of the robotic system in real-time , parallel processing is necessary to mini- mize the computation time using algorithms dedicated to parallel computing and implemented on multiprocessor network systems. In this context , two main approaches have been highlighted and tested. A first approach uses parallel computing ( approach Zomaya ) by breaking down the complete task into subtasks resulting from the dynamic model using the recursive algo- rithm NE. The subtasks are assigned to a number of processors belonging to a multiprocessor architecture. A second approach that seeks to minimize the computation time by proposing al- gorithms based on strategies of matrix decomposition and manipulation of the ynamic model in order to obtain a final decomposition for solving the system of equations the dynamic model( Fijani approach). In this second approach , the size of the problem determines the number of processors , if the robotic system has N dof , the network architecture requires N processors . It allows a computational complexity of O(log N). The thesis includes a significant investigations and many contributions . Note the following few elements : 1. Solving the problem of distribution of contact forces on robot anipulators under grasping constraints and without slip of the manipulated object . Constraints on the object have been included in the problem of optimal distribution of effort between the two arms by minimizing a quadratic cost criterion. 2. The formulations of the dynamics and control of overall coordination in the operational space of a system multirobots manipulating an object in space. In this sense a simulator in Matlab was developed which allowed us to test the model and finally simulations were used to illustrate the results of the proposed approach. 3. Exploitation of parallel computing approach by decomposition and allocation of tasks to a multiprocessor system where the number of processors is chosen by the user ( Zomaya approach ) . The simulations were performed using Matlab, emulation and visualization of the implementation of the decomposition algorithm were developed in Labview . Finally an estimate of the computing time comparing multiprocessor to monoprocessor has been derived. 4. Exploitation of parallel computing approach for matrix decomposition and allocation of tasks to a multiprocessor system where the number of processors is imposed by the size of the system ( approach Fijani). An illustrative example is given. action of robots with the object to manipulate in its environment . A major constraint appears here because of the computation time becomes prohibitive and does not allow for real-time control of a cooperative group of robots. This is why , in the second place , it is necessary to contribute in exploring and mplementing serial and parallel computing approaches. But also to accelerate the computation time for simulation and applications requiring control and real time coordination. This can be done by implementing parallel computing algorithms dedicated to network of processors as currently permitted by the transputer technology and DSP (Digital Signal Processing), clusters and supercomputers. Restricted to cases of serial robot manipula- tors in cooperation , an analysis of the state of the art as well as the results of our research has highlighted the following elements : a) - In terms of dynamic modeling , although the models of Newton - Lagrange and Newton- Euler have been developed for serial systems in open-chains , they are adaptable and generalized for cooperating robot manipulators systems . However, if the number of robots exceeds 3 robots of 6 DOF each, the mathematical formalism is difficult to organize and exploit because of the big size of symbolic expressions for the equations of the model. b ) - For the control of the robotic system in real-time , parallel processing is necessary to mini- mize the computation time using algorithms dedicated to parallel computing and implemented on multiprocessor network systems. In this context , two main approaches have been highlighted and tested. A first approach uses parallel computing ( approach Zomaya ) by breaking down the complete task into subtasks resulting from the dynamic model using the recursive algo- rithm NE. The subtasks are assigned to a number of processors belonging to a multiprocessor architecture. A second approach that seeks to minimize the computation time by proposing al- gorithms based on strategies of matrix decomposition and manipulation of the dynamic model in order to obtain a final decomposition for solving the system of equations the dynamic model ( Fijani approach). In this second approach , the size of the problem determines the number of processors , if the robotic system has N dof , the network architecture requires N processors . It allows a computational complexity of O(log N). The thesis includes a significant investigations and many contributions . Note the following few elements : 1. Solving the problem of distribution of contact forces on robot manipulators under grasping constraints and without slip of the manipulated object . Constraints on the object have been included in the problem of optimal distribution of effort between the two arms by minimizing a quadratic cost criterion. 2. The formulations of the dynamics and control of overall coordination in the operational space of a system multirobots manipulating an object in space. In this sense a simulator in Matlab was developed which allowed us to test the model and finally simulations were used to illustrate the results of the proposed approach. 3. Exploitation of parallel computing approach by decomposition and allocation of tasks to a multiprocessor system where the number of processors is chosen by the user ( Zomaya approach ) . The simulations were performed using Matlab, emulation and visualization of the implementation of the decomposition algorithm were developed in Labview . Finally an estimate of the computing time comparing multiprocessor to monoprocessor has been derived. 4. Exploitation of parallel computing approach for matrix decomposition and allocation of tasks to a multiprocessor system where the number of processors is imposed by the size of the system ( approach Fijani). An illustrative example is given.