Table of Contents. Chapter 1. Modeling and Identification of Serial Robots... 1 Wisama KHALIL and Etienne DOMBRE

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1 Chapter 1. Modeling and Identification of Serial Robots Wisama KHALIL and Etienne DOMBRE 1.1. Introduction Geometric modeling Geometric description Direct geometric model Inverse geometric model Stating the problem Principle of Paul s method Kinematic modeling Direct kinematic model Calculation of the Jacobian matrix by derivation of the DGM Kinematic Jacobian matrix Decomposition of the kinematic Jacobian matrix into three matrices Dimension of the operational space of a robot Inverse kinematic model General form of the kinematic model Inverse kinematic model for the regular case Solution at the proximity of singular positions Inverse kinematic model of redundant robots... 24

2 vi Modeling, Performance Analysis and Control of Robot Manipulators 1.4. Calibration of geometric parameters Introduction Geometric parameters Geometric parameters of the robot Parameters of the robot s location Geometric parameters of the end-effector Generalized differential model of a robot Principle of geometric calibration General form of the calibration model Identifying the geometric parameters Solving the identification equations Calibration methods of geometric parameters Calibration model by measuring the end-effector location Autonomous calibration models Correction of geometric parameters Dynamic modeling Lagrange formalism General form of dynamic equations Calculation of energy Properties of the dynamic model Taking into consideration the friction Taking into account the inertia of the actuator s rotor Taking into consideration the forces and moments exerted by the end-effector on its environment Newton-Euler formalism Newton-Euler equations linear in the inertial parameters Practical form of Newton-Euler equations Determining the base inertial parameters Identification of dynamic parameters Introduction Identification principle of dynamic parameters Solving method Identifiable parameters Choice of identification trajectories Evaluation of joint coordinates Evaluation of joint torques... 65

3 vii Identification model using the dynamic model Sequential formulation of the dynamic model Practical considerations Conclusion Bibliography Chapter 2. Modeling of Parallel Robots Jean-Pierre MERLET and François PIERROT 2.1. Introduction Characteristics of classic robots Other types of robot structure General advantages and disadvantages Present day uses Simulators and space applications Industrial applications Medical applications Precise positioning Machine types Introduction Plane robots with three degrees of freedom Robots moving in space Manipulators with three degrees of freedom Manipulators with four or five degrees of freedom Manipulators with six degrees of freedom Inverse geometric and kinematic models Inverse geometric model Inverse kinematics Singular configurations Singularities and statics State of the art The geometric method Maneuverability and condition number Singularities in practice

4 viii Modeling, Performance Analysis and Control of Robot Manipulators 2.4. Direct geometric model Iterative method Algebraic method Reminder concerning algebraic geometry Planar robots Manipulators with six degrees of freedom Bibliography Chapter 3. Performance Analysis of Robots Philippe WENGER 3.1. Introduction Accessibility Various levels of accessibility Condition of accessibility Workspace of a robot manipulator General definition Space of accessible positions Primary space and secondary space Defined orientation workspace Free workspace Calculation of the workspace Concept of aspect Definition Mode of aspects calculation Free aspects Application of the aspects Concept of connectivity Introduction Characterization of n-connectivity Characterization of t-connectivity Local performances Definition of dexterity Manipulability Isotropy index

5 ix Lowest singular value Approach lengths and angles Conclusion Bibliography Chapter 4. Trajectory Generation Moussa HADDAD, Taha CHETTIBI, Wisama KHALIL and Halim LEHTIHET 4.1. Introduction Point-to-point trajectory in the joint space under kinematic constraints Fifth-order polynomial model Trapezoidal velocity model Smoothed trapezoidal velocity model Point-to-point trajectory in the task-space under kinematic constraints Trajectory generation under kinodynamic constraints Problem statement Constraints Objective function Description of the method Outline Construction of a random trajectory profile Handling kinodynamic constraints Summary Trapezoidal profiles Examples Case of a two dof robot Optimal free motion planning problem Optimal motion problem with geometric path constraint Case of a six dof robot Optimal free motion planning problem Optimal motion problem with geometric path constraints

6 x Modeling, Performance Analysis and Control of Robot Manipulators Optimal free motion planning problem with intermediate points Conclusion Bibliography Appendix: Stochastic Optimization Techniques Chapter 5. Position and Force Control of a Robot in a Free or Constrained Space Pierre DAUCHEZ and Philippe FRAISSE 5.1. Introduction Free space control Hypotheses applying to the whole chapter Complete dynamic modeling of a robot manipulator Ideal dynamic control in the joint space Ideal dynamic control in the operational working space Decentralized control Sliding mode control Robust control based on high order sliding mode Adaptive control Control in a constrained space Interaction of the manipulator with the environment Impedance control Force control of a mass attached to a spring Non-linear decoupling in a constrained space Position/force hybrid control Parallel structure External structure Specificity of the force/torque control Conclusion Bibliography

7 xi Chapter 6. Visual Servoing François CHAUMETTE 6.1. Introduction Modeling visual features The interaction matrix Eye-in-hand configuration Eye-to-hand configuration Interaction matrix Interaction matrix of a 2-D point Interaction matrix of a 2-D geometric primitive Interaction matrix for complex 2-D shapes Interaction matrix by learning or estimation Interaction matrix related to 3-D visual features Pose estimation Interaction matrix related to θu Interaction matrix related to a 3-D point Interaction matrix related to a 3-D plane Task function and control scheme Obtaining the desired value s Regulating the task function Case where the dimension of s is 6 (k = 6) Case where the dimension of s is greater than 6 (k > 6) Hybrid tasks Virtual links Hybrid task function Target tracking Other exteroceptive sensors Conclusion Bibliography

8 xii Modeling, Performance Analysis and Control of Robot Manipulators Chapter 7. Modeling and Control of Flexible Robots Frédéric BOYER, Wisama KHALIL, Mouhacine BENOSMAN and George LE VEY 7.1. Introduction Modeling of flexible robots Introduction Generalized Newton-Euler model for a kinematically free elastic body Definition: formalism of a dynamic model Choice of formalism Kinematic model of a free elastic body Balance principle compatible with the mixed formalism Virtual power of the field of acceleration quantities Virtual power of external forces Virtual power of elastic cohesion forces Balance of virtual powers Linear rigid balance in integral form Angular rigid balance in integral form Elastic balances in integral form Linear rigid balance in parametric form Intrinsic matrix form of the generalized Newton-Euler model Velocity model of a simple open robotic chain Acceleration model of a simple open robotic chain Generalized Newton-Euler model for a flexible manipulator Extrinsic Newton-Euler model for numerical calculus Geometric model of an open chain Recursive calculation of the inverse and direct dynamic models for a flexible robot Introduction Recursive algorithm of the inverse dynamic model Recursive algorithm of the direct dynamic model Iterative symbolic calculation Control of flexible robot manipulators Introduction Reminder of notations

9 xiii Control methods Regulation Point-to-point movement in fixed time Trajectory tracking in the joint space Trajectory tracking in the operational space Conclusion Bibliography List of Authors Index