Belief Space Planning Simplified: Trajectory-Optimized LQG (T-LQG) (Extended Report)
This work addresses computational efficiency in belief space planning for robotics and autonomous systems, though it appears incremental as it builds on existing LQG and NLP methods.
The paper tackles the high-dimensional belief space planning problem under motion and observation uncertainties by reducing it from (n^2+n) to (n) dimensions using a Linear Quadratic Gaussian (LQG) design optimized for nominal performance, and solves it via a Non-Linear Program (NLP) with proven validity under approximations, achieving the lowest computational burden among major methods.
Planning under motion and observation uncertainties requires solution of a stochastic control problem in the space of feedback policies. In this paper, we reduce the general (n^2+n)-dimensional belief space planning problem to an (n)-dimensional problem by obtaining a Linear Quadratic Gaussian (LQG) design with the best nominal performance. Then, by taking the underlying trajectory of the LQG controller as the decision variable, we pose a coupled design of trajectory, estimator, and controller design through a Non-Linear Program (NLP) that can be solved by a general NLP solver. We prove that under a first-order approximation and a careful usage of the separation principle, our approximations are valid. We give an analysis on the existing major belief space planning methods and show that our algorithm has the lowest computational burden. Finally, we extend our solution to contain general state and control constraints. Our simulation results support our design.