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# Newton-Euler inverse dynamics

> How a forward pass of twists and a backward pass of wrenches compute the joint torques for a desired robot-arm motion.

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Inverse dynamics determines the joint torques that make a robot arm follow a desired motion. You will develop the recursive Newton-Euler algorithm by following sections 8.3 and 8.4 of Lynch and Park (book pages 289 and 293) (Kevin M. Lynch, 2017). Its forward pass carries twists and their rates from the base to the tip, using the adjoint to change frames. The backward pass carries wrenches from the tip to the base. Combining these passes gives the closed form $\tau = M(\theta)\ddot\theta + c(\theta, \dot\theta) + g(\theta)$. The derivation uses the single-body equations from [rigid-body dynamics](/aiml-common/lectures/dynamics/rigid-body-dynamics/index) and the adjoint from [calculus on Lie groups](/aiml-common/lectures/motion-algebras/lie-calculus/index).

## References

* Kevin M. Lynch, F. (2017). *Modern Robotics*.

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