 Underactuated Robotics by Russ Tedrake

Author-hosted book: underactuated.mit.edu/

Consulted chapter: 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: 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; 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. ^[ref]

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.