Summer School-Mathematical Methods in Robotics, 13-31 July 2009Syllabus

Geometric Methods in RoboticsPart II: Robotic Manipulation

Lecture Syllabus

ByZ.X. Li∗ and Y.Q. Wu#

∗Dept. of ECE, Hong Kong University of Science & Technology#School of ME, Shanghai Jiaotong University

20-31 July 2009

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A. Brief history on geometric methods in Robotics

♢ Geometric Tools

1 Euclid (�. 300BC)

2 C. F. Gauss (1777-1855)

3 B. Riemann (1826-1866)

4 S. Lie (1842-1899)

5 E. Cartan (1869-1951)

6 H. Weyl (1885-1955)

7 S.S. Chern (1911-2004)

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Books/Lecture notes:1 W. M. Boothby. An introduction to di�erentiable manifolds and Riemannian

geometry. Pure and applied mathematics. Academic Press, Orlando, rev. 2ndedition, 2002.

2 H. Lowe. Summer School: Mathematical Methods in Robotics—Part I∼IV. TUBraunschweig, Institute Computational Mathematics, 2009.

♢ Robotics1 F. Reuleaux (1829-1905)

2 R. Brockett

3 J. Herve

Books:1 R. M. Murray, Z. X. Li, and S. S. Sastry. A mathematical introduction to robotic

manipulation. CRC Press, Boca Raton, 1994.2 J. M. Selig. Geometric fundamentals of robotics.Springer, New York, 2005.

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Papers:1 R. W. Brockett. Robotic manipulators and the product of exponentials formula.

Lecture Notes in Control and Information Sciences, pages 120–129, 1984.2 J. Loncaric. Geometric analysis of compliant mechanism in robotics. Harvard

University PhD�esis, 1985.3 B. Paden and S. S. Sastry. Optimal kinematic design of 6r manipulators.

International Journal of Robotics Research, 7(2):43–61, 1988.4 M. Buss, L. Faybusovich, and J. B. Moore. Dikin-type algorithms for dextrous

grasping force optimization. International Journal of Robotics Research, 17(8):831–839,1998.

5 J. M. Selig. Curvature in force/position control. In Robotics and Automation, 1998.Proceedings. 1998 IEEE International Conference on, volume 2, pages 1761–1766 vol.2,1998.

6 D. J. Montana. �e Kinematics of Contact and Grasp. In International Journal ofRobotics Research, volume 7(3), pages 17–32, 1988.

7 Z. X. Li, J. B. Gou, and Y. X. Chu Geometric algorithms for workpiece localizationIEEE Transactions on Robotics and Automation, 14(6):864–878, 1998.

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7 S. R. Ploen and F. C. Park. Coordinate-invariant algorithms for robot dynamics.IEEE Transactions on Robotics and Automation, 15(6):1130–1135, 1999.

8 G. F. Liu, Y. J. Lou, and Z. X. Li. Singularities of parallel manipulators: a geometrictreatment. IEEE Transactions on Robotics and Automation, 19(4):579–594, 2003.

9 L. Han, J. C. Trinkle, and Z. X. Li. Grasp analysis as linear matrix inequalityproblems. IEEE Transactions on Robotics and Automation, 16(6):663–674, 2000.

10 G. F. Liu and Z. X. Li. A uni�ed geometric approach to modeling and control ofconstrained mechanical systems. Robotics and Automation, IEEE Transactions on,18(4):574–587, 2002.

11 G. F. Liu and Z. X. Li. Real-time grasping-force optimization for multi�ngeredmanipulation: �eory and experiments. IEEE/ASME Transactions on Mechatronics,9(1):65–77, 2004.

12 J. Meng, G. Liu, and Z. Li. A geometric theory for analysis and synthesis of sub-6 dofparallel manipulators. IEEE Transactions on Robotics, 23(4):625–649, 2007.

13 Y. Q. Wu, Z. X. Li, H. Ding and Y. J. Lou. Quotient kinematics machines: Concept,analysis and synthesis. In Intelligent Robots and Systems, 2008. IROS 2008. IEEE/RSJInternational Conference on, pages 1964–1969, 2008.

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♢Motivations A general language & tool for analyzing and solvingengineering problems, especially those in robotics,control, manufacturing, etc.

♢ A Sample List of Problems1 Kinematics, dynamics and control ofopen/closed chain manipulators

2 Kinematics and force optimization of robotichands

3 Holonomic/Nonholonomic motion planning4 Computer vision (Ma Yi, S.S. Sastry, etc. ⟨Aninvitation to 3D vision⟩)

5 Mechanism synthesis and design6 workpiece localization and tolerancing7 ⋮

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B. Open-chain manipulators and multi�ngered robotic hands(implicit use of the geometric concepts in Prof. Lowe’s lecturenotes)

Lecture 1 Rigid body motion (SO(3), SE(3), their Liealgebras, the exponential map, velocity vectors,connections with classic screw theory)Subgroups and Submanifolds of SE(3)

Lecture 2 Kinematics of open-chain manipulators—Forward kinematics (canonical coordinates ofsecond kind)—Inverse kinematics (Paden-Kahansubproblem)—Jacobian & Singularities

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Lecture 3 Dynamics of open-chain manipulators—Rigid body dynamics (Newton-Euler equationin body frame)—Lagrangian formulation—Coordinate invariant algorithms

Lecture 4 Kinematics of multi�ngered robotic hands—Contact model—�e grasp map—Contact kinematics—Grasping force optimization—Coordinated control

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C. Advanced Applications (explicit use of the geometric conceptsin Prof. Lowe’s lecture notes)

Lecture 5 Workpiece Localization & Tolerancing�eory—Regular workpiece—Symmetric workpiece (homogeneous spaces)—Hybrid workpiece—Tolerancing and inspection

Lecture 6 Parallel Mechanisms—Singularities—Synthesis—Quotient Kinematics Machines

Lecture 7 Control of constrained manipulationLecture 8 Nonholonomic motion planning