Modelling and Control

This first volume in the series is based on part of a course that I taught in various state and private institutions during 1979 and 1980. It was concerned with the design and control of stationary, articulated robots operating as non-feedback systems. This book (which is devoted to the statement and understanding of problems rather than their solution) presents a review of some of the work, started in 1972, of the team involved with robotics and biomechanics at the Automation Laboratory at Montpellier, in association with the French National Centre for Scientific Research. I am greatly indebted to Professor A. Liegeois, the guiding light of the team, to A. Fournier, E. Dombre, W. Khalil, P. Molinier and P. Borrel who have contributed so much to the progress made in this field. The second volume will describe the present state of the knowledge of robotic systems which are able to perceive the environment, to a greater or lesser extent, and to react appropriately. Such robots will be able to perform the function required of them, in spite of unpredictable, limited changes in the environment. The third volume will deal with teleoperations, the branch of robotics characterized by the necessary and almost permanent presence of a human operator at the controls. The fourth volume will be concerned with technological components of robots and further volumes will discuss robotic languages and programming methods, decision autonomy and artificial intelligence and, finally, the computer-aided design of robots.

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1 Definitions and objectives.- Origin of the word 'robot'.- Robotics today.- What is a robot?.- Classification of robots.- Conclusions.- 2 Structure and specification of articulated robots.- Degrees of freedom of a solid.- Degrees of freedom of a robot.- Position of the vehicle and resulting redundancy of degrees of freedom.- How many degrees of freedom?.- False degrees of freedom.- Architecture of the arm.- Description of articulated mechanical systems.- Conclusions.- 3 Articulated mechanical systems: determination of kinematic elements.- Computation of the orientation of a chain relative to a set bound to an upper segment.- Computation of the orientation of a chain relative to a set bound to a lower segment.- Computation of the position of a point on a chain in relation to an upper segment.- Computation of the position of a point on a chain in relation to a lower segment.- Determination of the velocity vectors of rotation of different segments of a chain relative to a set of coordinate axes.- Determination of the velocity vectors of translation of different segments of a chain relative to a set of coordinate axes.- Conclusions.- 4 Calculation of robot articulation variables.- The absence of a solution.- An infinite number of solutions.- A limited number of solutions.- Practical choice of [Pi(R0), Sj(R0)].- Mechanisms with six degrees of freedom.- Mechanisms with more than six degrees of freedom.- Conclusions.- 5 Positional control of articulated robots.- Reference and starting configurations.- The principles of positional control.- Balanced and initialization configurations.- The problems associated with positional control.- 6 Speed control of articulated robots.- The principles of speed control.- Problems arising from the use of equation (6-16).- Methods ofresolving redundant systems.- Conclusions.- 7 Articulated mechanical systems: the dynamic model.- A dynamic model for an open articulated chain of rigid segments, without backlash or friction.- Development of a dynamic equation for a system having three degrees of freedom.- Another type of model: the bond graph.- Difficulties with dynamic models.- A dynamic model of a belt drive.- Conclusions.- 8 Dynamic control of articulated robots.- Problems associated with real time and computation.- Simplification of the equation of the model.- Other methods of dynamic control.- The choice of the space used in computation.- Conclusions.- 9 Learning and trajectory generation.- Methods of recording trajectories.- Manual control used outside of training.- Improved controls.- Trajectory generation.- Conclusions.- 10 Tasks and performance of articulated robots.- Description of tasks.- The performance of articulated robots.- Conclusions.- References.