Update: Nathan 2018-12-07

1. Quick weekly updates
  • Gave MS presentation and submitted associated project report
  • Met with Honeywell to discuss spherical motor
  • Worked on paper for MPC class (hopefully to be submitted to a conference after revisions from Borrelli)
2. Detailed updates

Mark mentioned that we would be getting a new undergrad in the lab that may be able to work on some project involving the spherical motor (e.g. a CMG quadcopter), and I’ll also be meeting with a prospective (?) masters student (Jackie) at the end of next week to discuss what we do in the lab. I’ve starting thinking ways to use the spherical motor besides attaching it to the momentum wheel in order to make it a CMG (I think there might be some novel vehicle that utilizes it well).

The paper I’m writing for my MPC class is less about MPC and more about optimization. The working title is “Simultaneous Trajectory Generation and Ranging Measurement Selection for Mobile Systems”. The working abstract is as follows:

We present an optimization-based method for generating chance constrained trajectories and sequences of desired ranging measurements for mobile systems.
A system model is presented that uses an Extended Kalman Filter (EKF) to estimate the vehicle state using ranging measurements from a set of base stations at known locations, where the vehicle is only able to range with a subset of the base stations during a single time step.
The trajectory generation and base station selection problems are solved simultaneously with a mixed-integer nonlinear program.
The resulting trajectories and ranging measurement sequences satisfy state and input constraints with some desired probability while minimizing a given objective function.
Simulations are presented that verify the approach and show an improvement over methods that consider the trajectory generation and ranging measurement selection problems separately.

I have written about half of the paper. It is useful because it includes the choice of ranging target as a decision variable in the planning step, allowing for more aggressive trajectories that are subject to chance constraints (i.e. the trajectory will not exceed the state constraints with some probability given by the user). An example of when this is useful is when a vehicle is moving down a narrow corridor. The vehicle would prefer to take ranging measurements that decrease its position uncertainty in the direction of the walls in order to avoid collisions. There has not yet been a method presented in the literature that accomplishes this, and furthermore I think this paper includes interesting ideas about how to include decisions that affect your state estimation (i.e. how to deal with measurements that  depend on some decision variables).

I won’t go too into the weeds here, but I’d like to get feedback from Mark on the paper once I completed a full draft (probably after finals, the paper is due Dec. 17th).

Lessons learned

I’ve read a lot about dealing with chance constraints in uncertain systems and how to properly model how uncertainly propagates through a system in closed loop. I’ve also spent a good amount of time looking into different optimization solvers and modeling languages. I’ve decided to use pyomo as a modeling language and BONMIN as the underlying MI-NLP solver for the optimization problem I am solving in my paper. I spent some time looking into using CPLEX, but it can’t handle nonlinear constraints (except for quadratic constraints, I think)

3. Planned work for next week
  • Finish writing paper for MPC class and submit to Borrelli to grade/review
  • Meet with students working in lab next semester
4. Planned work for next month
  • Decide on next research project
  • Come up with projects for new lab members (e.g. a novel vehicle design that uses the spherical motor or additional uses for momentum wheel vehicle/folding arms vehicle)