The Parallelization of Riccati Recursion
This addresses a bottleneck in robotic trajectory optimization by providing a faster method for generating feedback policies, though it is incremental as it builds on known dynamic-programming approaches.
The paper tackles the slow computation of solutions to linear-quadratic optimal control problems for complex robots by parallelizing Riccati recursion, enabling faster solutions while still generating feedback control policies, and empirically shows it outperforms existing parallel methods.
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.