# LQR-trees with Sampling Based Exploration of the State Space

## TL;DR

This paper enhances the LQR-tree algorithm by integrating a sampling-based exploration method, enabling more reliable synthesis of feedback control laws for complex systems from diverse initial conditions.

## Contribution

It introduces a randomized motion-planning approach to improve demonstration generation in the LQR-tree algorithm, expanding its applicability.

## Key findings

- More reliable feedback control synthesis for complex systems.
- Effective exploration of uncharted state space regions.
- Enhanced performance over previous LQR-tree implementations.

## Abstract

This paper introduces an extension of the LQR-tree algorithm, which is a feedback-motion-planning algorithm for stabilizing a system of ordinary differential equations from a bounded set of initial conditions to a goal. The constructed policies are represented by a tree of exemplary system trajectories, so called demonstrations, and linear-quadratic regulator (LQR) feedback controllers. Consequently, the crucial component of any LQR-tree algorithm is a demonstrator that provides suitable demonstrations. In previous work, such a demonstrator was given by a local trajectory optimizer. However, these require appropriate initial guesses of solutions to provide valid results, which was pointed out, but largely unresolved in previous implementations. In this paper, we augment the LQR-tree algorithm with a randomized motion-planning procedure to discover new valid demonstration candidates to initialize the demonstrator in parts of state space not yet covered by the LQR-tree. In comparison to the previous versions of the LQR-tree algorithm, the resulting exploring LQR-tree algorithm reliably synthesizes feedback control laws for a far more general set of problems.