A Mathematical Introduction to Robotic Manipulation

By Richard M. Murray, S. Sastry, Zexiang Li. 1994

INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

Subfields: Robotics & Control

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Citations in the corpus

Causal Models for Dynamical Systems (2020, methodology): “In Pfister et al. [2018a] we propose a procedure that specifically exploits the invari ance of Equation (36.”
Learning stable and predictive structures in kinetic systems (2018, methodology): “, n}, we perform a regression to find a function g ∈M such that [4] is optimized across all repetitions k belonging to different experiments than i.”
Deep visual foresight for planning robot motion (2016, methodology): “Standard model-based methods for robotic manipulation might involve estimating the physical properties of the environment, and then solving for the controls based on the known laws of physics [4], [5], [6].”
Dexterous Manipulation with Deep Reinforcement Learning: Efficient, General, and Low-Cost (2018, background): “While considerable progress has been made on the theoretical side [9], sensing and estimation challenges have limited their applicability in the real world considerably.”
Learning Depth from Monocular Videos Using Direct Methods (2017, methodology): “where rotation matrix R is computed from exponential coordinates ω by the Rodrigues’ formula [25]; x̃i is the homogeneous coordinate for xi; and 〈·〉 projects 3D points to the image plane: 〈”
A data-driven approach for real-time full body pose reconstruction from a depth camera (2011, background): “Through forward kinematics [17] using χ, joint positions Pχ ∈ R 3×J”
A Review of Human Activity Recognition Methods (2015, methodology): “Human actions are treated as curves in the Lie group (Murray et al., 1994), and the classification was performed using SVM and temporal modeling approaches.”
3D-based Deep Convolutional Neural Network for action recognition with depth sequences (2016, background): “In this way, human actions can be modeled as curves in a Lie group [32].”
Human Action Recognition by Representing 3D Skeletons as Points in a Lie Group (2014, methodology): “We refer the readers to [4] for a general introduction to Lie groups and [11] for further details on SE(3) and rigid body kinematics.”
Planning algorithms (2006, methodology): “, a robot hand may have fingers with spherical tips); see [105, 679, 728, 732].”
A way of relating instantaneous and finite screws based on the screw triangle product (2017, methodology): “By utilizing matrix groups to describe finite motions of rigid body systems, Brockett [31] applied the exponential map between Lie group SE(3) and Lie algebra se(3) to relating models for finite motions to that for instantaneous motions [32].”
Robots in machining (2019, background): “The Jacobian contains parts for the linear velocity Jv and the angular velocity Jv, which are described exemplary for rotational joints in the following equations [9]:”
Self-Organizing Feature Maps for Modeling and Control of Robotic Manipulators (2003, background): “As a matter of fact, Murray et al. (1994) pointed out that our impatience with the pace of robotics research and our expectations of what robots can and cannot do is in large part due to our lack of appreciation of the incredible power and subtlety of our own biological motor control systems.”
Elastic functional coding of human actions: From vector-fields to latent variables (2015, background): “For efficient implementations of a general exponential and inverse exponential maps between any two arbitrary points, we refer the reader to [15].”
An Overview of Dexterous Manipulation (1999, background): “For a detailed treatment of this topic see [19, 28, 30].”
The Vectorial Parameterization of Rotation (2003, unknown): “keywords: Finite rotations, Parameterization of rotations.”