Real-Time Stochastic Optimal Control for Multi-Agent Quadrotor Systems

Abstract

This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as velocity sequences, and a platform-specific low-level controller which ensures that these velocity sequences are met. The planning task is expressed as a centralized path-integral control problem, for which optimal control computation corresponds to a probabilistic inference problem that can be solved by efficient sampling methods. Through simulation we show that our SOC approach (a) has significant benefits compared to deterministic control and other SOC methods in multimodal problems with noise-dependent optimal solutions, (b) is capable of controlling a large number of platforms in real-time, and (c) yields collective emergent behaviour in the form of flight formations. Finally, we show that our approach works for real platforms, by controlling a team of three quadrotors in outdoor conditions.

Physics-Informed Representation and Learning: Control and Risk Quantification

“…Previous work on stochastic optimal control deals with diverse uncertainty and randomness, but these methods are not efficient for high-dimensional systems because forward rollouts and backward dynamic programming requires computation that scales exponentially with the dimension of the state (Gorodetsky, Karaman, and Marzouk 2018;Frankowska and Zhang 2020). Previous studies on stochastic safe control aim to control the level of risk in the system and ensure the probability of safety does not decay over time (Samuelson and Yang 2018;Gómez et al 2016). These methods rely on accurate estimations of the probability of risk in the system, and standard methods for such risk estimation are computationally heavy, especially for highdimensional systems.…”

Feature-Based MPPI Control with Applications to Maritime Systems

“…While in general the resulting optimal feedback control function has an unknown structure, there are different approaches for its representation. Besides reinforcement learning (RL) approaches based on offline learning a parametrized policy [6,7], NMPC has become the de-facto technological standard [8,9]. Based on path integrals, a new type of sample-based NMPC algorithm was presented in [8].…”

“…Besides reinforcement learning (RL) approaches based on offline learning a parametrized policy [6,7], NMPC has become the de-facto technological standard [8,9]. Based on path integrals, a new type of sample-based NMPC algorithm was presented in [8]. Using a free energy definition described in [10] and [11], the input affine requirement is completely removed by [4].…”