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Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization

This seems to be a well-known paper about trajectory optimization. Think of this paper whenever I see the software package called "trajopt." In fact, this has more citations than the TRPO paper as of today, though the TRPO one will likely surpass it by mid-2018 at the latest.

Anyway, let's get to the main purpose of the paper. What is it? It's to find good trajectories for robots during motion planning, and the key here is to avoid collisions in a fast, scalable, robust way. There's a decent introduction to trajectory optimization here, which emphasizes the need for optimizing (which here we use sequential convex optimization) and checking collisions (signed distances here).

They say they don't deal with dynamic constraints (see Section III) but what does that actually mean??

Sequential Convex Optimization, this definition makes sense:

Sequential convex optimization solves a non-convex optimization problem by repeatedly constructing a convex subproblem --— an approximation to the problem around the current iterate x. The subproblem is used to generate a step ∆x that makes progress on the original problem.

The algorithm is actually important enough that it was discussed in CS 287 Fall 2015, when I took it. They use quadratic programming to approximate the subproblem in a convex manner.

The parts about managing constraints, dealing with signed distances, etc., seem reasonable. There's some novel stuff in Section V, I assume, about dealing with continuous time constraints. Why is this important? Because at each time step they consider, the robot will be collision-free from their previous algorithm. BUT ... the time steps are effectively discretized, so the continuous motion from A(t) to A(t+1) means that intermediate points risk running into collisions.

Experiments:

  • MoveIt!. This is simulation.

  • PR2. This is real-life.

  • Atlas Humanoid Robot. This has the most DOF so it's the most challenging in theory, but it's a simulation compared to the reality of the PR2. Still, it's challenging!

The videos are quite informative. Check them out on the paper website.

They show that their algorithms are superior to competing methods.

To review/learn:

  • CHOMP
  • STOMP

Yeah, I forgot how these work since I've been getting distracted with Deep Learning lately. But CHOMP is related to Hamiltonian Monte Carlo in some way.