Mobile Robotics

Luc Jaulin is Professor in robotics at ENSTA-Bretagne in France. He conducts research at the Lab-STICC in the field of submarine robotics and sailing robots using set methods.

• Introduction ixChapter 1. Three-dimensional Modeling 11.1. Rotation matrices 11.1.1. Definition 21.1.2. Lie group 31.1.3. Lie algebra 41.1.4. Rotation vector 51.1.5. Adjoint 61.1.6. Rodrigues rotation formulas 71.1.7. Coordinate system change 81.2. Euler angles 111.2.1. Definition 111.2.2. Rotation vector of a moving Euler matrix 131.3. Inertial unit 141.4. Dynamic modeling 171.4.1. Principle 171.4.2. Modeling a quadrotor 181.5. Exercises 201.6. Corrections 37Chapter 2. Feedback Linearization 652.1. Controlling an integrator chain 652.1.1. Proportional-derivative controller 662.1.2. Proportional-integral-derivative controller 672.2. Introductory example 682.3. Principle of the method 692.3.1. Principle 692.3.2. Relative degree 712.3.3. Differential delay matrix 722.3.4. Singularities 732.4. Cart 752.4.1. First model 752.4.2. Second model 762.5. Controlling a tricycle 782.5.1. Speed and heading control 782.5.2. Position control 802.5.3. Choosing another output 812.6. Sailboat 822.6.1. Polar curve 832.6.2. Differential delay 832.6.3. The method of feedback linearization 842.6.4. Polar curve control 872.7. Sliding mode 872.8. Kinematic model and dynamic model 902.8.1. Principle 902.8.2. Example of the inverted rod pendulum 912.8.3. Servo-motors 942.9. Exercises 952.10. Corrections 107Chapter 3. Model-free Control 1333.1. Model-free control of a robot cart 1343.1.1. Proportional heading and speed controller 1343.1.2. Proportional-derivative heading controller 1363.2. Skate car 1373.2.1. Model 1383.2.2. Sinusoidal control 1403.2.3. Maximum thrust control 1403.2.4. Simplification of the fast dynamics 1423.3. Sailboat 1453.3.1. Problem 1453.3.2. Controller 1463.3.3. Navigation 1523.3.4. Experiment 1533.4. Exercises 1553.5. Corrections 168Chapter 4. Guidance 1834.1. Guidance on a sphere 1834.2. Path planning 1874.2.1. Simple example 1874.2.2. Bézier polynomials 1884.3. Voronoi diagram 1894.4. Artificial potential field method 1914.5. Exercises 1924.6. Corrections 201Chapter 5. Instantaneous Localization 2215.1. Sensors 2215.2. Goniometric localization 2255.2.1. Formulation of the problem 2255.2.2. Inscribed angles 2265.2.3. Static triangulation of a plane robot 2285.2.4. Dynamic triangulation 2295.3. Multilateration 2305.4. Exercises 2315.5. Corrections 236Chapter 6. Identification 2436.1. Quadratic functions 2436.1.1. Definition 2436.1.2. Derivative of a quadratic form 2446.1.3. Eigenvalues of a quadratic function 2456.1.4. Minimizing a quadratic function 2456.2. The least squares method 2466.2.1. Linear case 2466.2.2. Nonlinear case 2486.3. Exercises 2506.4. Corrections 253Chapter 7. Kalman Filter 2637.1. Covariance matrices 2637.1.1. Definitions and interpretations 2637.1.2. Properties 2667.1.3. Confidence ellipse 2677.1.4. Generating Gaussian random vectors 2687.2. Unbiased orthogonal estimator 2697.3. Application to linear estimation 2747.4. Kalman filter 2757.5. Kalman–Bucy 2797.6. Extended Kalman filter 2827.7. Exercises 2837.8. Corrections 298Chapter 8. Bayes Filter 3298.1. Introduction 3298.2. Basic notions of probabilities 3298.3. Bayes filter 3328.4. Bayes smoother 3348.5. Kalman smoother 3358.5.1. Equations of the Kalman smoother 3358.5.2. Implementation 3368.6. Exercises 3378.7. Corrections 345References 359Index 361