Layered Control Architecture for 6-Agent Escort Formation ($SE(3)$ Homogeneous Sheaf)

This example demonstrates scaling the layered control architecture to a 6-agent formation escorting a slow-moving target in 3D space using an $SE(3)$ Homogeneous Affine Cellular Sheaf.

High-Level API

We use the new Formations and DistributedLayeredControl modules to significantly simplify the setup of the escort ring and the execution of the distributed local controllers.

using CellularSheaves
using CellularSheaves.Formations
using CellularSheaves.AgentControllers
using CellularSheaves.DistributedLayeredControl
using LinearAlgebra
using Statistics
using Distributed
using Plots
using Printf

A single house style for every figure below

default(framestyle = :box, grid = true, gridalpha = 0.18, gridstyle = :dot,
    titlefontsize = 10, guidefontsize = 9, legendfontsize = 8, tickfontsize = 8,
    markerstrokewidth = 0, size = (720, 380))

const RING_COLOR = :steelblue
const TARGET_COLOR = :black

:black

Setup 10D Quadrotor Dynamics & DARE Solver

dyn = QuadrotorDynamics()
DT = 0.05
nx = 10

10

Compute Optimal LQR Gain via Discrete Algebraic Riccati Equation (DARE)

Q_diag = [500.0, 500.0, 500.0, 150.0, 150.0, 100.0, 100.0, 100.0, 5.0, 5.0]
Q_lqr = Matrix(Diagonal(Q_diag))
R_lqr = Matrix(Diagonal([0.005, 0.005, 0.005]))

lqr_controller = LQRController(dyn, DT, Q_lqr, R_lqr)
K_lqr = lqr_controller.K

3×10 Matrix{Float64}:
 0.0       0.0      21.0723  0.0      0.0      0.0      0.0     10.4824  0.0       0.0
 0.0      -1.46667   0.0     2.39227  0.0      0.0     -1.0703   0.0     0.255503  0.0
 1.46667   0.0       0.0     0.0      2.39227  1.0703   0.0      0.0     0.0       0.255503

SE(3) Homogeneous Coordination Sheaf Construction (D = 4)

6 agents in a single escort ring.

const NA = 6
const NT = 1
const TV1 = NA + 1
r_ring = 0.3

0.3

Build the escort ring, with Agent 1 pinned as the observer

sheaf = build_escort_ring(NA, TV1, r_ring; observers=[1])

A network sheaf with 7 vertex stalks and 7 edge stalks.

Fast-moving target trajectory

target1_pos(node, t) = [0.5cos(0.5*t), 0.5sin(0.5*t), 1.5 + 0.1sin(1.0*t), 1.0]

target1_pos (generic function with 1 method)

Provision Worker Processes

Provision exactly NA worker processes (one for each agent's flight computer). Workers start with stderr detached: a worker inherits the parent's stderr, which while these docs are built is the pipe capturing the page's output, and holding it open stalls the build. Each worker still reports through its stdout, which the parent relays.

workers_pids = redirect_stderr(devnull) do
    addprocs(NA; exeflags = ["--project=$(Base.active_project())",
        "--sysimage=$(unsafe_string(Base.JLOptions().image_file))"])
end

6-element Vector{Int64}:
  5
  6
  7
  8
  9
 10

Provide the cellular sheaves environment to all workers

@everywhere workers_pids begin
    using CellularSheaves
end

Simulation Framework

STEPS = 200
epsilon = 0.02

0.02

Start agents in a line along the x-axis

init_states = [[r_ring*i/NA, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] for i in 1:NA]

6-element Vector{Vector{Float64}}:
 [0.049999999999999996, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.09999999999999999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.15, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.19999999999999998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]

Create heterogeneous agent properties (varying mass and inertia)

dyns = [QuadrotorDynamics(m=0.5 + 0.05*i, Ixx=0.01 + 0.002*i, Iyy=0.01 + 0.002*i) for i in 1:NA]
K_lqrs = [LQRController(d, DT, Q_lqr, R_lqr).K for d in dyns]
agent_configs = [(init_states[i], dyns[i], K_lqrs[i]) for i in 1:NA]

prob = LayeredControlProblem(sheaf, [TV1], target1_pos, agent_configs, DT, STEPS, r_ring)

CellularSheaves.ControlSheaves.DistributedLayeredControl.LayeredControlProblem(A network sheaf with 7 vertex stalks and 7 edge stalks.
, [7], Main.var"##1658".target1_pos, nothing, nothing, Tuple{Vector{Float64}, CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics, Matrix{Float64}}[([0.049999999999999996, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.55, 0.012, 0.012), [0.0 0.0 23.155681190378882 0.0 0.0 0.0 0.0 11.519911616866297 0.0 0.0; 0.0 -1.7599735965077932 0.0 2.870686340109049 0.0 0.0 -1.2843436264323052 0.0 0.30659989356367856 0.0; 1.7599735965077927 0.0 0.0 0.0 2.8706863401090486 1.2843436264323052 0.0 0.0 0.0 0.30659989356367856]), ([0.09999999999999999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.6, 0.014, 0.014), [0.0 0.0 25.232354358509784 0.0 0.0 0.0 0.0 12.554408254133824 0.0 0.0; 0.0 -2.0532605811338844 0.0 3.349078558831746 0.0 0.0 -1.4983720900987731 0.0 0.3576954723740814 0.0; 2.0532605811338835 0.0 0.0 0.0 3.3490785588317467 1.498372090098773 0.0 0.0 0.0 0.3576954723740814]), ([0.15, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.65, 0.016, 0.016), [0.0 0.0 27.301777873345102 0.0 0.0 0.0 0.0 13.585644127011617 0.0 0.0; 0.0 -2.3465282100371168 0.0 3.8274451665066107 0.0 0.0 -1.712387261425324 0.0 0.40878901933445405 0.0; 2.3465282100371163 0.0 0.0 0.0 3.827445166506611 1.7123872614253237 0.0 0.0 0.0 0.4087890193344541]), ([0.19999999999999998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.7, 0.018000000000000002, 0.018000000000000002), [0.0 0.0 29.36341085933043 0.0 0.0 0.0 0.0 14.613375885779773 0.0 0.0; 0.0 -2.6397737216488646 0.0 4.30578250903451 0.0 0.0 -1.92638724392375 0.0 0.459880244545805 0.0; 2.6397737216488633 0.0 0.0 0.0 4.3057825090345085 1.9263872439237484 0.0 0.0 0.0 0.45988024454580495]), ([0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.75, 0.02, 0.02), [0.0 0.0 31.41672665850292 0.0 0.0 0.0 0.0 15.637366559271296 0.0 0.0; 0.0 -2.932994355813146 0.0 4.784086934163531 0.0 0.0 -2.140370142072015 0.0 0.5109688582551377 0.0; 2.932994355813146 0.0 0.0 0.0 4.784086934163528 2.140370142072015 0.0 0.0 0.0 0.5109688582551376]), ([0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.8, 0.022, 0.022), [0.0 0.0 33.46121357508947 0.0 0.0 0.0 0.0 16.657385889028156 0.0 0.0; 0.0 -3.2261873539624526 0.0 5.262354791718899 0.0 0.0 -2.354334061434512 0.0 0.5620545708736221 0.0; 3.2261873539624535 0.0 0.0 0.0 5.2623547917189 2.3543340614345123 0.0 0.0 0.0 0.5620545708736221])], 0.05, 200, 0.3, 3)

Run distributed simulation

init_distributed_agents!(workers_pids, agent_configs, DT, epsilon)
sim_d_res = run_layered_simulation(prob, workers_pids; mode=:distributed)

CellularSheaves.ControlSheaves.DistributedLayeredControl.LayeredSimulationResult(CellularSheaves.ControlSheaves.DistributedLayeredControl.LayeredControlProblem(A network sheaf with 7 vertex stalks and 7 edge stalks.
, [7], Main.var"##1658".target1_pos, nothing, nothing, Tuple{Vector{Float64}, CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics, Matrix{Float64}}[([0.049999999999999996, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.55, 0.012, 0.012), [0.0 0.0 23.155681190378882 0.0 0.0 0.0 0.0 11.519911616866297 0.0 0.0; 0.0 -1.7599735965077932 0.0 2.870686340109049 0.0 0.0 -1.2843436264323052 0.0 0.30659989356367856 0.0; 1.7599735965077927 0.0 0.0 0.0 2.8706863401090486 1.2843436264323052 0.0 0.0 0.0 0.30659989356367856]), ([0.09999999999999999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.6, 0.014, 0.014), [0.0 0.0 25.232354358509784 0.0 0.0 0.0 0.0 12.554408254133824 0.0 0.0; 0.0 -2.0532605811338844 0.0 3.349078558831746 0.0 0.0 -1.4983720900987731 0.0 0.3576954723740814 0.0; 2.0532605811338835 0.0 0.0 0.0 3.3490785588317467 1.498372090098773 0.0 0.0 0.0 0.3576954723740814]), ([0.15, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.65, 0.016, 0.016), [0.0 0.0 27.301777873345102 0.0 0.0 0.0 0.0 13.585644127011617 0.0 0.0; 0.0 -2.3465282100371168 0.0 3.8274451665066107 0.0 0.0 -1.712387261425324 0.0 0.40878901933445405 0.0; 2.3465282100371163 0.0 0.0 0.0 3.827445166506611 1.7123872614253237 0.0 0.0 0.0 0.4087890193344541]), ([0.19999999999999998, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.7, 0.018000000000000002, 0.018000000000000002), [0.0 0.0 29.36341085933043 0.0 0.0 0.0 0.0 14.613375885779773 0.0 0.0; 0.0 -2.6397737216488646 0.0 4.30578250903451 0.0 0.0 -1.92638724392375 0.0 0.459880244545805 0.0; 2.6397737216488633 0.0 0.0 0.0 4.3057825090345085 1.9263872439237484 0.0 0.0 0.0 0.45988024454580495]), ([0.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.75, 0.02, 0.02), [0.0 0.0 31.41672665850292 0.0 0.0 0.0 0.0 15.637366559271296 0.0 0.0; 0.0 -2.932994355813146 0.0 4.784086934163531 0.0 0.0 -2.140370142072015 0.0 0.5109688582551377 0.0; 2.932994355813146 0.0 0.0 0.0 4.784086934163528 2.140370142072015 0.0 0.0 0.0 0.5109688582551376]), ([0.3, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], CellularSheaves.ControlSheaves.AgentControllers.QuadrotorDynamics(9.81, 0.8, 0.022, 0.022), [0.0 0.0 33.46121357508947 0.0 0.0 0.0 0.0 16.657385889028156 0.0 0.0; 0.0 -3.2261873539624526 0.0 5.262354791718899 0.0 0.0 -2.354334061434512 0.0 0.5620545708736221 0.0; 3.2261873539624535 0.0 0.0 0.0 5.2623547917189 2.3543340614345123 0.0 0.0 0.0 0.5620545708736221])], 0.05, 200, 0.3, 3), [0.05025635306433698 0.1001860262522584 0.15006411530239802 0.1999937955507906 0.25002664725578755 0.3001110788407213; 0.05371421673452679 0.10269719358362983 0.15093305651525 0.19991612815962548 0.2503934701640751 0.30161786861965034; 0.06458851596781354 0.11061408873657079 0.15370800166202703 0.1997338677958589 0.25162318331435335 0.30644397773297777; 0.0846534104807252 0.12525464828853594 0.15889742312011676 0.19949919221045814 0.25401811893349047 0.31549517573242; 0.11361929270851286 0.14641933254672743 0.1664501386219327 0.19925093181150513 0.2575905180130497 0.3286988609860483; 0.15001728980810117 0.17303618820440936 0.17598353731598895 0.19900336616851472 0.26216669310352164 0.34540097612776605; 0.19185595420181195 0.20364437402564964 0.18696301945071675 0.19875249101022208 0.2674819610513003 0.3646805318550805; 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Run centralized simulation

init_distributed_agents!(workers_pids, agent_configs, DT, epsilon)
sim_c_res = run_layered_simulation(prob, workers_pids; mode=:centralised)

divergence = maximum(abs.(sim_d_res.sim_data .- sim_c_res.sim_data))
@printf("Max divergence between centralized and distributed 6-agent simulation: %.3e\n", divergence)

Max divergence between centralized and distributed 6-agent simulation: 4.752e-14

Clean up worker processes

rmprocs(workers_pids)

Task (done) @0x00007fe2a045ad10

Multi-Projection Trajectory & Attitude Dynamics Visualization

We can now easily animate the simulation using the Plots.jl recipe framework. The animate_layered_escort function abstracts away the complex multi-panel visualization. (Note: this relies on the CellularSheavesPlots package extension)

animate_layered_escort(sim_d_res; frame_step = 4, filename = "layered_escort_tracking.gif", fps = 10)
nothing # hide

[ Info: Saved animation to /home/runner/work/CellularSheaves.jl/CellularSheaves.jl/docs/src/generated/layered/layered_escort_tracking.gif