Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty

Abstract

This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets.The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.

Robust Space Trajectory Design Using Belief Optimal Control

“…The solution of the BOC is an open-loop control profile which is the most robust and reliable against the effects of uncertainty. This work builds on and extends previous research on optimal control under epistemic uncertainty [31,32]. In [32] the authors introduced a new multiple shooting transcription approach for trajectory optimisation under uncertainty.…”

“…This work builds on and extends previous research on optimal control under epistemic uncertainty [31,32]. In [32] the authors introduced a new multiple shooting transcription approach for trajectory optimisation under uncertainty. The new transcription approach was capable of handling a wide range of uncertainty models (parametric, non-parametric, imprecise set of distributions, etc.…”

“…This section presents an efficient multiple shooting-like direct transcription method for the solution of problem (16), which employs a direct propagation of the belief state. This work generalises the direct transcription method developed in [32] to the case in which orbit determination arcs intermingle control arcs and a fully intrusive uncertainty propagation is not possible.…”

Robust Bayesian Particle Filter for Space Object Tracking Under Severe Uncertainty

“…Intrusive polynomial algebra could be employed in place of non-intrusive alternatives when the dynamical model can be accessed and templated, as it provides good performance and scalability for high-dimensional problems [29] and it proved effective for uncertainty propagation in space applications [30].…”

Reinforcement Learning for Robust Trajectory Design of Interplanetary Missions

“…9,10 Also, the robust design of a low-thrust interplanetary transfer to a near-Earth asteroid was performed by using evidence theory to model epistemic uncertainties in the performance of the main thruster and in the magnitude of the departure hyperbolic excess velocity. 11 Belief-based transcription procedures for the stochastic optimal control problem were proposed for the robust design of space trajectories under stochastic and epistemic uncertainties, 12,13 incorporating also navigation analysis in the formulation to update the knowledge of the spacecraft state in presence of observations. 14…”