Robot dynamics

Level AdvancedDifficulty ★★★★★Application⌖ Open in the map

What is it?

How torques produce motion: the Euler–Lagrange equations of the Lagrangian $\mathcal L = T - V$ give $M(q)\ddot q + C(q,\dot q)\dot q + g(q) = \tau$ , a system of second-order ODEs simulated and inverted by controllers.

Formulas

\frac{\dd}{\dd t}\frac{\partial\mathcal L}{\partial\dot q_i} - \frac{\partial\mathcal L}{\partial q_i} = \tau_i

M(q)\,\ddot q + C(q,\dot q)\,\dot q + g(q) = \tau

The mathematics behind it

Systems of ODEs★★★★★frequent
A robot's equations of motion $M(q)\ddot q + C(q,\dot q)\dot q + g(q) = \tau$ form a coupled system.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

⚙ Robotics and control

Trajectory optimization and MPC★★★★★

What depends on it

Trajectory optimization and MPC

This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.