Class 06 - Q&A

[andrewrosemberg]

Forum for questions about the external seminar held in class 06.

[andrewrosemberg]

Tora.jl uses Semi-implicit Euler for the discretization/integrator approach. How does this compare to the other approaches discussed in the previous lectures? (e.g. Explicit and Implicit Euler; Explicit Runge-Kutta, Implicit Trapezoidal Collocation, ...)

[andrewrosemberg]

From what I can see, Tora.jl uses a zero-order hold for the control variables (torques). Does this make too much of a difference for robotic arms in practice?

How about if we were solving for a legged robot that perhaps needs smoother controls?

[andrewrosemberg]

Instead of representing collocation points and the dynamics inside the trajectory optimization problem, Tora.jl uses constraint transcription: It calls an external Newton-Euler algorithm method to solve the dynamics function for a given knot variable value, uses ForwardDiff Automatic Differentiation to compute the Jacobians and Hessians of this constraint, and subsequently provides it to the trajectory optimization solver.

What are the advantages and disadvantages of this approach? If you had more time, would you implement differently?

[ArnaudDeza]

In the direct transcription method, on slide 20 we have the constraints for system dynamics, contact forces and task requirements.

I am wondering if it's common to also have constraints that act as safety (or more like coherence) constraints between two close discrete time points. i.e joint angles/velocity between two discrete points cannot change too abruptly or too strongly? Maybe this is a silly question as it's already handled in the physics that is baked into the system dynamics?

[andrewrosemberg]

Following up on our conversation in class, the constraint transcription used does not allow for constraints on the collocation points AFAIK. However, since we chose how the control evolves, we can somehow control this for systems that are well-behaved.