bjack205 / bilinearcontrol.jl Goto Github PK

• Control bounds
• State bounds

COSMOAccelerators

Add an example optimizing the kinematics of SE(3)

Allow use of iterative solvers like MINRES to solve the inner optimization problems.

• Read COSMO paper
• Look up nonlinear ADMM solvers

Attitude control is bilinear if the angular velocity is a control input.
Add the following examples

• fully actuated body
• body with control about only 2 axes

Each example should have a method to generate a prototypical QP to be solved when applying SQP.

• Pendulum
• Cartpole
• Bilinear Pendulum
• Bilinear Cartpole

QUESTION: What is the exact QP we should be solving? Should the objective include the Hessian of the Lagrangian?

COSMO uses safeguarding on their accelerators. Try implementing their safeguard checks to see if it makes the performance improvement more reliable.

Implement the penalty tuning from this paper.

Add a version of the solver special-cased to the quadrotor MPC problem.
Look into generating custom expressions / functions to fill in Ahat and Bhat or the Jacobian-vector products.

Use the formula in Boyd's book to automatically adapt the penalty parameter.

Define a suite of benchmark linear systems.

• Double integrator swarm
• linearization of SE2(3) quadrotor
• linearization of swarm of dubins cars

Use relaxation method from Boyd's paper.

Can maybe use an expanded vector to create a bilinear system for a rigid body.
Need to store quadratic terms in omega and cross terms between linear and angular velocity

• Solve pendulum swing-up with ALTRO
• Track pendulum swing-up with bilinear TVLQR
• Track pendulum swing-up with bilinear MPC

Use the consensus form of trajopt ADMM to solve the trust-region problem with box constraints on the controls and norm constraints on the states.

Use Riccati to solve the modified unconstrained problem.