Computing Dynamics

Forward Dynamics

Given $\theta$, $\dot{\theta}$, $\tau$ -> Find $\ddot{\theta}$

Can be solved using:

1. Lagrangian Formulation
2. Newton-Euler (explicit or implicit)
3. (rare) Hamiltons Principle of Least Action

Implicit methods are iterative.

Issues with semi-implicit Euler:

• high rates can prove a challenge for control tasks, such as model-predictive control applications where real-time re-planning is required
• or reinforcement- learning settings where vanishing or exploding gradients are exacerbated over long horizons with many time steps

Inverse Dynamics

Given $\theta$, $\dot{\theta}$, $\ddot{\theta}$ -> Find $\tau$

Continuous vs. Discrete Mechanics

Variational Integrator Approach automatically conserves momentum and energy.

Setting in which you're operating determines whether you care about this conservation of momentum feature or not.