Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Corridor MPC for Multi-Agent Inspection of Orbiting Structures

Gregorio Marchesini, Pedro Roque, Dimos V. Dimarogonas

Abstract

In this work, we propose an extension of the previously introduced Corridor Model Predictive Control scheme for high-order and distributed systems, with an application for on-orbit inspection. To this end, we leverage high order control barrier function (HOCBF) constraints as a suitable control approach to maintain each agent in the formation within a safe corridor from its reference trajectory. The recursive feasibility of the designed MPC scheme is tested numerically, while suitable modifications of the classical HOCBF constraint definition are introduced such that safety is guaranteed both in sampled and continuous time. The designed controller is validated through computer simulation in a realistic inspection scenario of the International Space Station.

Corridor MPC for Multi-Agent Inspection of Orbiting Structures

Abstract

In this work, we propose an extension of the previously introduced Corridor Model Predictive Control scheme for high-order and distributed systems, with an application for on-orbit inspection. To this end, we leverage high order control barrier function (HOCBF) constraints as a suitable control approach to maintain each agent in the formation within a safe corridor from its reference trajectory. The recursive feasibility of the designed MPC scheme is tested numerically, while suitable modifications of the classical HOCBF constraint definition are introduced such that safety is guaranteed both in sampled and continuous time. The designed controller is validated through computer simulation in a realistic inspection scenario of the International Space Station.
Paper Structure (10 sections, 2 theorems, 35 equations, 3 figures, 2 tables)

This paper contains 10 sections, 2 theorems, 35 equations, 3 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. BACKGROUND
  3. Nonlinear Relative Dynamics
  4. High Order Control Barrier Functions
  5. PROBLEM STATEMENT
  6. SAMPLED DATA HOCBF
  7. CONTROL STRATEGY
  8. Corridor MPC
  9. RESULTS
  10. CONCLUSIONS AND FUTURE WORK

Key Result

Lemma 1

Consider the perturbed control affine system eq:perturbed nonlinear system where the functions $\bm{g} :\mathbb{R}^{n} \times \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}^{n \times m}$ and $\bm{f} : \mathbb{R}^{n} \times \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}^{n}$ are at least $C^{r+1}$ in $\tilde where $L_w$ is defined over the set $\mathcal{Q}\triangleq\mathbb{D}\times\mathbb{U}\times\mathbb{W

Figures (3)

  • Figure 1: Relative state of the inspector spacecraft ($\delta \bm{r}$) with respect to the a general SV ($\bm{r}_{sv}$). The Hill's frame is defined by the base $\{\hat{\bm{r}},\hat{\bm{s}},\hat{\bm{w}}\}$ while the inertial frame $\mathcal{J}$ is defined by $\{\hat{\bm{e}}_1,\hat{\bm{e}}_2,\hat{\bm{e}}_3\}$.
  • Figure 2: Time evolution of the CBFs $h_{\delta \bm{v}}$,$h_{\delta \bm{r}}$; the HOCBF nominal function $\zeta_{\delta \bm{r}}$,$\zeta_{\delta \bm{v}}$; and the control signal $\|\bm{u}\|_2$ for each inspector.
  • Figure 3: Three PRO assigned to each inspector around the ISS. The base directions are given in terms of the LVLH frame where $\hat{\bm{r}}$ is the radial direction, $\hat{\bm{s}}$ is the along-track direction and $\hat{\bm{w}}$ is the cross-track direction.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Lemma 1
  • proof
  • Definition 3
  • Lemma 2
  • proof
  • Definition 4: SD-HOCBF