Spatial Shape Sensing

Collecting some references and notes here related to converting local curvature measurements (e.g. with FBG sensors) to global estimates of applied force or deflection.

• Leonard Meirovitch, Methods of analytical dynamics, Courier Dover Publications, 2004 ISBN 0486432394, 9780486432397 (various editions, actually).
  • Some pages for maths for 3D rotations and their derivatives ("velocities" and "accelerations" in dynamics = orientations and curvatures in differential geometry)
• Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, Inc., 2005, ISBN-13: 9780471488859
  • Some pages on curves, tangents, curvature, torsion and the Frenet-Serret apparatus
  • also related to the Darboux frame in differential geometry of curves, surfaces

• Cutkosky's thesis book

@book{Cutkosky85,
 author = {Mark R. Cutkosky},
 title = {Robotic Grasping and Fine Manipulation},
 year = {1985},
 isbn = {0898382009},
 publisher = {Kluwer Academic Publishers},
 address = {Norwell, MA, USA},
 }

• Pages from appendix on differential transformations and curvature (applied to rolling)

appendix - rolling contact uses parametric curves and their derivatives in matrix notation.

-- MarkCutkosky - 06 Aug 2008