OTaHSCube - Optimal Tasks and Heater Scheduling Applied to CubeSats

OTaHSCube is a Julia package dedicated to energy and temperature-aware task scheduling for quality-of-service assurance in CubeSats

Dependencies

• Julia
• JuMP
• Gurobi
• JLD

Usage

Main file

jobs = 7 # insert here number of tasks/jobs, excluding the heater task
T = 48 # insert here time horizon / orbit duration

just_plot = false # define if this execution aims only to plot an already obtained result

if !just_plot
    include("params.jl")
    include("examples/$(T)_$(jobs).jl")
    include("fvm_temp_checker.jl")
    include("model.jl")
else
    #import vars here
    include("plot.jl")

Parameters file

The parameters.jl file is a julia lang file containing the following definitions:

Variable (Code)	Variable (Paper)	Definition
M	$M$	a large number which would not be part of any optimal solution, used in big-M constraints
q	$Q$	nominal battery capacity (in Ah)
soc0	$SoC_1$	initial battery SoC
lower_bound	$\rho$	minimum accepted battery SoC
bat_usage	$\gamma$	maximum charge/discharge battery current (in Ampères)
ef	$e$	battery charge/discharge efficiency
v_bat	$V_b$	battery voltage

Example file

The (T)_(jobs).jl file is a julia lang file containing the following definitions:

Variable (Code)	Variable (Paper)	Definition
jobs	$J$	number of jobs
T	$T$	time horizon
resource_p	$r_t$	vector containing the available resource for each time instant
min_duration	$t_j^{\min}$	vector containing the minimum duration of each job
max_duration	$t_j^{\max}$	vector containing the maximum duration of each job
min_period_job	$p_j^{\min}$	vector containing the minimum period for each job
max_period_job	$p_j^{\max}$	vector containing the maximum period for each job
min_statup	$y_j^{\min}$	vector containing the minimum number of startups for each job
max_statup	$y_j^{\max}$	vector containing the maximum number of startups for each job
win_min	$w_j^{\min}$	minimum time window for each job
win_max	$w_j^{\max}$	maximum time window for each job
priority	$u_j$	vector containing the priority of each job
use_p	$q_j$	vector containing the power usage of each job

Example 48_7 parameters

$j$	1	2	3	4	5	6	7	8 (heater)
$u_j$	7	2	4	3	5	1	6	0
$q_j$	2.39	0.80	0.76	1.13	2.49	0.76	1.17	1.00
$y_j^{\min}$	1	1	1	2	2	2	1	2
$y_j^{\max}$	1	4	2	4	3	2	2	6
$t_j^{\min}$	2	2	3	2	4	1	2	10
$t_j^{\max}$	10	3	12	10	5	3	2	49
$p_j^{\min}$	5	8	10	8	7	12	11	1
$p_j^{\max}$	47	17	27	22	30	43	43	49
$w_j^{\min}$	0	0	0	0	9	0	0	0
$w_j^{\max}$	48	48	48	48	44	48	48	48

Output files

Two output files are generated, namely:

• (T)_(jobs)_EN.pdf
  • Graph of: Energy balance (W; primary axis) and SoC (%; secondary axis) vs. time (min)
• (T)_(jobs)_SCH_TMP.pdf
  • Graph of: jobs/tasks activations ($x$) vs. time

References

Library inspired by Cezar Augusto Rigo`s task scheduling papers.

1. Rigo, C. A.; Seman, L. O.; Camponogara, E.; Morsch Filho, E.; Bezerra; E. A . . Task scheduling for optimal power management and quality-of-service assurance in CubeSats. ACTA Astronautica, v. 179, p. 550-560, 2021.

2. Rigo, C. A. ; Seman, L. O. ; Camponogara, E. ; Morsch Filho, E. ; Bezerra, E. A. . A nanosatellite task scheduling framework to improve mission value using fuzzy constraints. EXPERT SYSTEMS WITH APPLICATIONS, v. 175, p. 114784, 2021.

3. Rigo, C. A. ; Seman, L. O. ; Camponogara, E. ; Morsch Filho, E. ; Bezerra, E. A. ; Munari Junior, P. A. . A branch-and-price algorithm for nanosatellite task scheduling to improve mission quality-of-service. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2022.

How to cite

BibTex

@misc{OTaHSCube,
title = {Optimal tasks and heater scheduling applied to the management of CubeSats battery lifespan},
author = {Brenda Fernandes Ribeiro, Laio Oriel Seman, Cezar Antonio Rigo, Eduardo Camponogara},
url = {https://github.com/b-rib/OTaHSCube}
}