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Note for Robotics and Robot Applications - RRA by Sunil Senthili

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2 Introduction to Robotics, Marc Toussaint—February 4, 2014 13 Exercises 69 14 Topic list 79

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Introduction to Robotics, Marc Toussaint—February 4, 2014 1 3 Introduction Why Robotics? 1:1 Why Robotics? • Commercial: 1:2 Industrial, health care, entertainment, agriculture, surgery, etc • Critical view: – International Committee for Robot Arms Control – Noel Sharkey’s articles on robot ethics (Child care robots PePeRo.. Robotics as intelligence research 1:3 AI in the real world AI: Machine Learning, probabilistic reasoning, optimization Real World: Interaction, manipulation, perception, navigation, etc 1:7 (robot “wife” aico) 1:4 Why AI needs to go real world

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4 Introduction to Robotics, Marc Toussaint—February 4, 2014 Newton-Euler, joint space control, reference trajectory following, optimal operational space control • Planning & optimization goal: planning around obstacles, optimizing trajectories Path finding vs. trajectory optimization, local vs. global, Dijkstra, Probabilistic Roadmaps, Rapidly Exploring Random Trees, differential constraints, metrics; trajectory optimization, general cost function, task variables, transition costs, gradient methods, 2nd order methods, Dynamic Pro- Tunicates digest their brain once they settled! • Motion was the driving force to develop intelligence – motion needs control & decision making ↔ fast information processing – motion needs anticipation & planning – motion needs perception gramming • Control Theory theory on designing optimal controllers Topics in control theory, optimal control, HJB equation, infinite horizon case, Linear-Quadratic – motion needs spatial representations optimal control, Riccati equations (differential, algebraic, discrete-time), controllability, stability, • Manipulation requires to acknowledge the structure (geometry, eigenvalue analysis, Lyapunov function physics, objects) of the real world. Classical AI does not 1:8 • Mobile robots goal: localize and map yourself Robotics as intelligence research • Machine Learning and AI are computational disciplines, which had great success with statistical modelling, analysis of data State estimation, Bayes filter, odometry, particle filter, Kalman filter, Bayes smoothing, SLAM, joint Bayes filter, EKF SLAM, particle SLAM, graph-based SLAM sets, symbolic reasoning. But they have not solved autonomous 1:11 learning, acting & reasoning in real worlds. • Neurosciences and psychology are descriptive sciences, either on the biological or cognitive level, e.g. with geat sucesses to describe and cure certain deceases. But they are not sufficient • Is this a practical or theoretical course? to create intelligent systems. • Robotics is the only synthetic discipline to understand intelli- “There is nothing more practical than a good theory.” (Vapnik, others...) gent behavior in natural worlds. Robotic tells us what the actual problems are when trying to organize behavior in natural worlds. 1:9 History • Essentially, the whole course is about reducing real-world problems to mathematical problems that can be solved efficiently 1:12 • Books There is no reference book for this lecture. But a basic wellknown standard text book is: 1:10 Four chapters • Kinematics & Dynamics goal: orchestrate joint movements for desired movement in task spaces Craig, J.J.: Introduction to robotics: mechanics and control. Addison-Wesley New York, 1989. (3rd edition 2006) Kinematic map, Jacobian, optimality principle of inverse kinematics, singularities, configura- 1:13 tion/operational/null space, multiple simultaneous tasks, special task variables, trajectory interpolation, motion profiles; 1D point mass, damping & oscillation, PID, general dynamic systems,

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6 Introduction to Robotics, Marc Toussaint—February 4, 2014 2 Kinematics Pose (position & orientation) Kinematic map, Jacobian, inverse kinematics as optimization problem, motion profiles, trajectory interpolation, multiple simultaneous tasks, special task variables, configuration/operational/null space, singularities • Two “types of robotics”: • A pose is described by a translation p ∈ R3 and a rotation R ∈ 1) Mobile robotics – is all about localization & mapping 2) Manipulation – is all about interacting with the world [0) Kinematic/Dynamic Motion Control: same as 2) without ever making it to interaction..] SO(3) – R is an orthonormal matrix (orthogonal vectors stay orthogonal, unit vectors stay unit) – R-1 = R⊤ – columns and rows are orthogonal unit vectors • Typical manipulation robots (and animals) are kinematic trees Their pose/state is described by all joint angles – det(R) = 1  R R12  11 – R=  R21 R 22  R31 R32  R13   R23   R33 2:1 2:5 Frame and coordinate transforms Basic motion generation problem • Move all joints in a coordinated way so that the endeffector makes a desired movement • Let (o, e1:3 ) be the world frame, (o′ , e′1:3 ) be the body’s frame. The new basis vectors are the columns in R, that is, e′1 = R11 e1 + R21 e2 + R31 e3 , etc, 01-kinematics: ./x.exe -mode 2/3/4 2:2 • x = coordinates in world frame (o, e1:3 ) x′ = coordinates in body frame (o′ , e′1:3 ) p = coordinates of o′ in world frame (o, e1:3 ) Outline x = p + Rx′ • Basic 3D geometry and notation 2:6 Rotations • Kinematics: φ : q 7→ y • Inverse Kinematics: y ∗ 7→ q ∗ = argminq ||φ(q)−y ∗ ||2C +||q−q0 ||2W • Basic motion heuristics: Motion profiles • Rotations can alternatively be represented as – Euler angles – NEVER DO THIS! – Rotation vector – Quaternion – default in code • Additional things to know – Many simultaneous task variables • See the “geometry notes” for formulas to convert, concatenate & apply to vectors – Singularities, null space, 2:7 2:3 Homogeneous transformations Basic 3D geometry & notation 2:4 • xA = coordinates of a point in frame A xB = coordinates of a point in frame B

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