  A method is presented for parallelizing the computation of solutions to
discrete-time, linear-quadratic, finite-horizon optimal control problems, which
we will refer to as LQR problems. This class of problem arises frequently in
robotic trajectory optimization. For very complicated robots, the size of these
resulting problems can be large enough that computing the solution is
prohibitively slow when using a single processor. Fortunately, approaches to
solving these type of problems based on numerical solutions to the KKT
conditions of optimality offer a parallel solution method and can leverage
multiple processors to compute solutions faster. However, these methods do not
produce the useful feedback control policies that are generated as a by-product
of the dynamic-programming solution method known as Riccati recursion. In this
paper we derive a method which is able to parallelize the computation of
Riccati recursion, allowing for super-fast solutions to the LQR problem while
still generating feedback control policies. We demonstrate empirically that our
method is faster than existing parallel methods.
