ABSTRACT
So far in the book we have focused on control of rigid-link robot arms, which have dynamics of the form https://www.w3.org/1998/Math/MathML"> M ( q ) q ¨ + V m ( q , q ˙ ) q ˙ + F ( q ˙ ) + G ( q ) + τ d = τ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062714/ecc29caf-77d7-4acc-990e-4f3c99184377/content/math5_0_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> or https://www.w3.org/1998/Math/MathML"> M ( q ) q ¨ + N ( q , q ˙ ) + τ d = τ , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062714/ecc29caf-77d7-4acc-990e-4f3c99184377/content/math5_0_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where https://www.w3.org/1998/Math/MathML"> N ( q , q ˙ ) ≡ V m ( q , q ˙ ) q ˙ + F ( q ˙ ) + G ( q ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062714/ecc29caf-77d7-4acc-990e-4f3c99184377/content/math5_0_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is the vector of the nonlinear terms. In these dynamics, M{q) is the inertia matrix, Vm (q,q̇) is the Coriolis/centripetal matrix, F(q̇) are the friction terms, G(q) is the gravity vector, and τd (t) represents disturbances. The rigid robot dynamics enjoy the properties in Chapter 3, which are reproduced here in Table 5.0.1.
