= Underactuated Robotics by Russ Tedrake
{c}
{tag=Work by Russ Tedrake}
Author-hosted book: https://underactuated.mit.edu/
Consulted chapter: https://underactuated.mit.edu/lqr.html
Chapter8, Linear Quadratic Regulators: Basic Derivation and Finite-horizon LQR, positive-semidefinite state costs, positive-definite control cost, HJB minimization and differential Riccati equation with terminal data. The page displays2024 and explicitly identifies the text as working course notes; no fixed publication year is asserted for the changing whole book.
Additional consulted chapters: https://underactuated.csail.mit.edu/humanoids.html , Center of pressure (CoP) and Zero-moment point (ZMP), The special case of flat terrain, defines the normal-force weighted ground point and distinguishes it from center-of-mass dynamics; https://underactuated.csail.mit.edu/multibody.html , Time-stepping LCP: Normal force, develops the nonnegative gap/reaction complementarity model. Its time-stepping block-collision discussion explicitly identifies the perfectly inelastic impact choice. Numerical loads, pressure profiles and lifting examples in the wiki are independent calculations.
The Multi-Body Dynamics chapter Compliant Contact Models section models normal contact with a stiff spring and optional damping, permits modeled penetration to generate force, and identifies stiffness of the resulting differential equations as a numerical integration difficulty. https://underactuated.mit.edu/multibody.html[Compliant Contact Models, spring response and stiff-system discussion]{ref}
https://underactuated.mit.edu/multibody.html[Multi-Body Dynamics, Contact modeling, contact Jacobian and generalized contact force equation]: the contact Jacobian maps generalized velocities to relative contact velocities, while its transpose maps contact forces into generalized forces. The scalar normal effective-inertia calculation in the wiki is an independent frozen-configuration derivation.
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