Theory of Robot Control

I Rigid manipulators.- 1 Modelling and identification.- 1.1 Kinematic modelling.- 1.1.1 Direct kinematics.- 1.1.2 Inverse kinematics.- 1.1.3 Differential kinematics.- 1.2 Dynamic modelling.- 1.2.1 Lagrange formulation.- 1.2.2 Newton-Euler formulation.- 1.2.3 Model computation.- 1.3 Identification of kinematic parameters.- 1.3.1 Model for identification.- 1.3.2 Kinematic calibration.- 1.3.3 Parameter identifiability.- 1.4 Identification of dynamic parameters.- 1.4.1 Use of dynamic model.- 1.4.2 Use of energy model.- 1.5 Further reading.- References.- 2 Joint space control.- 2.1 Dynamic model properties.- 2.2 Regulation.- 2.2.1 PD control.- 2.2.2 PID control.- 2.2.3 PD control with gravity compensation.- 2.3 Tracking control.- 2.3.1 Inverse dynamics control.- 2.3.2 Lyapunov-based control.- 2.3.3 Passivity-based control.- 2.4 Robust control.- 2.4.1 Constant bounded disturbance: integral action.- 2.4.2 Model parameter uncertainty: robust control.- 2.5 Adaptive control.- 2.5.1 Adaptive gravity compensation.- 2.5.2 Adaptive inverse dynamics control.- 2.5.3 Adaptive passivity-based control.- 2.6 Further reading.- References.- 3 Task space control.- 3.1 Kinematic control.- 3.1.1 Differential kinematics inversion.- 3.1.2 Inverse kinematics algorithms.- 3.1.3 Extension to acceleration resolution.- 3.2 Direct task space control.- 3.2.1 Regulation.- 3.2.2 Tracking control.- 3.3 Further reading.- References.- 4 Motion and force control.- 4.1 Impedance control.- 4.1.1 Task space dynamic model.- 4.1.2 Inverse dynamics control.- 4.1.3 PD control.- 4.2 Parallel control.- 4.2.1 Inverse dynamics control.- 4.2.2 PID control.- 4.3 Hybrid force/motion control.- 4.3.1 Constrained dynamics.- 4.3.2 Inverse dynamics control.- 4.3.3 Hybrid task specification and control.- 4.4 Further reading.- References.- II Flexible manipulators.- 5 Elastic joints.- 5.1 Modelling.- 5.1.1 Dynamic model properties.- 5.1.2 Reduced models.- 5.1.3 Singularly perturbed model.- 5.2 Regulation.- 5.2.1 Single link.- 5.2.2 PD control using only motor variables.- 5.3 Tracking control.- 5.3.1 Static state feedback.- 5.3.2 Two-time scale control.- 5.3.3 Dynamic state feedback.- 5.3.4 Nonlinear regulation.- 5.4 Further reading.- References.- 6 Flexible links.- 6.1 Modelling of a single-link arm.- 6.1.1 Euler-Bernoulli beam equations.- 6.1.2 Constrained and unconstrained modal analysis.- 6.1.3 Finite-dimensional models.- 6.2 Modelling of multilink manipulators.- 6.2.1 Direct kinematics.- 6.2.2 Lagrangian dynamics.- 6.2.3 Dynamic model properties.- 6.3 Regulation.- 6.3.1 Joint PD control.- 6.3.2 Vibration damping control.- 6.4 Joint tracking control.- 6.4.1 Inversion control.- 6.4.2 Two-time scale control.- 6.5 End-effector tracking control.- 6.5.1 Frequency domain inversion.- 6.5.2 Nonlinear regulation.- 6.6 Further reading.- References.- III Mobile robots.- 7 Modelling and structural properties.- 7.1 Robot description.- 7.1.1 Conventional wheels.- 7.1.2 Swedish wheel.- 7.2 Restrictions on robot mobility.- 7.3 Three-wheel robots.- 7.3.1 Type (3,0) robot with Swedish wheels.- 7.3.2 Type (3,0) robot with castor wheels.- 7.3.3 Type (2,0) robot.- 7.3.4 Type (2,1) robot.- 7.3.5 Type (1,1) robot.- 7.3.6 Type (1,2) robot.- 7.4 Posture kinematic model.- 7.4.1 Generic models of wheeled robots.- 7.4.2 Mobility, steerability and manoeuvrability.- 7.4.3 Irreducibility.- 7.4.4 Controllability and stabilizability.- 7.5 Configuration kinematic model.- 7.6 Configuration dynamic model.- 7.6.1 Model derivation.- 7.6.2 Actuator configuration.- 7.7 Posture dynamic model.- 7.8 Further reading.- References.- 8 Feedback linearization.- 8.1 Feedback control problems.- 8.1.1 Posture tracking.- 8.1.2 Point tracking.- 8.1.3 Velocity and torque control.- 8.2 Static state feedback.- 8.2.1 Omnidirectional robots.- 8.2.2 Restricted mobility robots.- 8.3 Dynamic state feedback.- 8.3.1 Dynamic extension algorithm.- 8.3.2 Differential flatness.- 8.3.3 Avoiding singularities.- 8.3.4 Solving the posture tracking problem.- 8.3.5 Avoiding singularities for Type (2,0) robots.- 8.4 Further reading.- References.- 9 Nonlinear feedback control.- 9.1 Unicycle robot.- 9.1.1 Model transformations.- 9.1.2 Linear approximation.- 9.1.3 Smooth state feedback stabilization.- 9.2 Posture tracking.- 9.2.1 Linear feedback control.- 9.2.2 Nonlinear feedback control.- 9.3 Path following.- 9.3.1 Linear feedback control.- 9.3.2 Nonlinear feedback control.- 9.4 Posture stabilization.- 9.4.1 Smooth time-varying control.- 9.4.2 Piecewise continuous control.- 9.4.3 Time-varying piecewise continuous control.- 9.5 Further reading.- References.- A Control background.- A.1 Lyapunov theory.- A. 1.1 Autonomous systems.- A.1.2 Nonautonomous systems.- A.1.3 Practical stability.- A.2 Singular perturbation theory.- A.3 Differential geometry theory.- A.3.1 Normal form.- A.3.2 Feedback linearization.- A.3.3 Stabilization of feedback linearizable systems.- A.4 Input-output.- A.4.1 Function spaces and operators.- A.4.2 Passivity.- A.4.3 Robot manipulators as passive systems.- A.4.4 Kalman-Yakubovich-Popov lemma.- A.5 Further reading.- References.