Traj opt 2DOF wing flapping

[avikde]

• implement dynamics
• compare discrete to cts
• animation
• flapping kinematics
• get osqp iteration to run
• initial trajectory is too infeasible to refine tol. try to make more feasible?
• factor the wingqp and the wing2dof model into a WingTrajOpt.py module
• function to animate these ~23 knot point trajectories

• Constraint: linearization of dynamics (as before). Nothing needs to change from the MPC module. This will set A, b for OSQP. Actuator constraints
  

• Objective: quadratic approx can be used for OSQP. Two choices: one needs Hessian, and one needs only Jacobian. See https://math.stackexchange.com/questions/2349026/why-is-the-approximation-of-hessian-jtj-reasonable One or both of these could be symbolically implemented and stored in Python (maybe using autograd) and OSQP update could update P, q.

Implementation

• Split up LTVMPC module into a LTVSystem: assembles A, b, has options for input, state, polytope constraints
• LTVMPC then needs a LTVSystem as one of its members (vs. a Model)
• For this, use as much of LTVMPC as possible,
• make a new module called SQP

[avikde]

For the dirtran optimization

First should try the simplest optimization (smallest dimension) and then slowly increase complexity.

• max lift s.t. constraints?
• change wing size s.t. actuator limits

[avikde]

Confirmed that the y2-dependence of the objective gradient is due to the appearance of psi (hinge angle) in the AoA. Fixing that results in y3-dependence only.

[avikde]

Manually rescaled by multiplying rows of A and the limits:

[avikde]

There is something somewhat wrong with the rescaling. When increasing it, the hinge angle wants to become higher, though the actual underlying dynamics should have not changed

[avikde]

Nonconvexity:

• think about the function and see if it makes sense
• can help it out by adding regularization (either damping or wx)\
• cost does improve when doing this

[avikde]

Right: desired hinge angle = 0; left: pi/4

EDIT: with increased force limit

Remember that there is a periodicity constraint. Accounting for that and dynamics, maybe this is somewhat working

[avikde]

Trying to do anything with the 2nd order lift approx as cost results in garbage like this

With outer prod of J

With hessian