153 lines
6.1 KiB
Matlab
153 lines
6.1 KiB
Matlab
function [obj] = constrainMotion(obj)
|
|
arguments (Input)
|
|
obj (1, 1) {mustBeA(obj, 'miSim')};
|
|
end
|
|
arguments (Output)
|
|
obj (1, 1) {mustBeA(obj, 'miSim')};
|
|
end
|
|
|
|
if size(obj.agents, 1) < 2
|
|
nAAPairs = 0;
|
|
else
|
|
nAAPairs = nchoosek(size(obj.agents, 1), 2); % unique agent/agent pairs
|
|
end
|
|
|
|
agents = [obj.agents{:}];
|
|
v = reshape(([agents.pos] - [agents.lastPos])./obj.timestep, 3, size(obj.agents, 1))';
|
|
|
|
% Initialize QP based on number of agents and obstacles
|
|
nAOPairs = size(obj.agents, 1) * size(obj.obstacles, 1); % unique agent/obstacle pairs
|
|
nADPairs = size(obj.agents, 1) * 5; % agents x (4 walls + 1 ceiling)
|
|
nLNAPairs = sum(obj.constraintAdjacencyMatrix, 'all') - size(obj.agents, 1);
|
|
total = nAAPairs + nAOPairs + nADPairs + nLNAPairs;
|
|
kk = 1;
|
|
A = zeros(total, 3 * size(obj.agents, 1));
|
|
b = zeros(total, 1);
|
|
|
|
% Set up collision avoidance constraints
|
|
h = NaN(size(obj.agents, 1));
|
|
h(logical(eye(size(obj.agents, 1)))) = 0; % self value is 0
|
|
for ii = 1:(size(obj.agents, 1) - 1)
|
|
for jj = (ii + 1):size(obj.agents, 1)
|
|
h(ii, jj) = norm(agents(ii).pos - agents(jj).pos)^2 - (agents(ii).collisionGeometry.radius + agents(jj).collisionGeometry.radius)^2;
|
|
h(jj, ii) = h(ii, jj);
|
|
|
|
A(kk, (3 * ii - 2):(3 * ii)) = -2 * (agents(ii).pos - agents(jj).pos);
|
|
A(kk, (3 * jj - 2):(3 * jj)) = -A(kk, (3 * ii - 2):(3 * ii));
|
|
b(kk) = obj.barrierGain * h(ii, jj)^3;
|
|
kk = kk + 1;
|
|
end
|
|
end
|
|
|
|
hObs = NaN(size(obj.agents, 1), size(obj.obstacles, 1));
|
|
% Set up obstacle avoidance constraints
|
|
for ii = 1:size(obj.agents, 1)
|
|
for jj = 1:size(obj.obstacles, 1)
|
|
% find closest position to agent on/in obstacle
|
|
cPos = obj.obstacles{jj}.closestToPoint(agents(ii).pos);
|
|
|
|
hObs(ii, jj) = dot(agents(ii).pos - cPos, agents(ii).pos - cPos) - agents(ii).collisionGeometry.radius^2;
|
|
|
|
A(kk, (3 * ii - 2):(3 * ii)) = -2 * (agents(ii).pos - cPos);
|
|
b(kk) = obj.barrierGain * hObs(ii, jj)^3;
|
|
|
|
kk = kk + 1;
|
|
end
|
|
end
|
|
|
|
% Set up domain constraints (walls and ceiling only)
|
|
% Floor constraint is implicit with an obstacle corresponding to the
|
|
% minimum allowed altitude, but I included it anyways
|
|
for ii = 1:size(obj.agents, 1)
|
|
% X minimum
|
|
h_xMin = (agents(ii).pos(1) - obj.domain.minCorner(1)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [-1, 0, 0];
|
|
b(kk) = obj.barrierGain * h_xMin^3;
|
|
kk = kk + 1;
|
|
|
|
% X maximum
|
|
h_xMax = (obj.domain.maxCorner(1) - agents(ii).pos(1)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [1, 0, 0];
|
|
b(kk) = obj.barrierGain * h_xMax^3;
|
|
kk = kk + 1;
|
|
|
|
% Y minimum
|
|
h_yMin = (agents(ii).pos(2) - obj.domain.minCorner(2)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [0, -1, 0];
|
|
b(kk) = obj.barrierGain * h_yMin^3;
|
|
kk = kk + 1;
|
|
|
|
% Y maximum
|
|
h_yMax = (obj.domain.maxCorner(2) - agents(ii).pos(2)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [0, 1, 0];
|
|
b(kk) = obj.barrierGain * h_yMax^3;
|
|
kk = kk + 1;
|
|
|
|
% Z minimum
|
|
h_zMin = (agents(ii).pos(3) - obj.domain.minCorner(3)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [0, 0, -1];
|
|
b(kk) = obj.barrierGain * h_zMin^3;
|
|
kk = kk + 1;
|
|
|
|
% Z maximum
|
|
h_zMax = (obj.domain.maxCorner(2) - agents(ii).pos(2)) - agents(ii).collisionGeometry.radius;
|
|
A(kk, (3 * ii - 2):(3 * ii)) = [0, 0, 1];
|
|
b(kk) = obj.barrierGain * h_zMax^3;
|
|
kk = kk + 1;
|
|
end
|
|
|
|
% Save off h function values (ignoring network constraints which may evolve in time)
|
|
obj.h(:, obj.timestepIndex) = [h(triu(true(size(obj.agents, 1)), 1)); reshape(hObs, [], 1); h_xMin; h_xMax; h_yMin; h_yMax; h_zMin; h_zMax;];
|
|
|
|
% Add communication network constraints
|
|
hComms = NaN(size(obj.agents, 1));
|
|
hComms(logical(eye(size(obj.agents, 1)))) = 0;
|
|
for ii = 1:(size(obj.agents, 1) - 1)
|
|
for jj = (ii + 1):size(obj.agents, 1)
|
|
if obj.constraintAdjacencyMatrix(ii, jj)
|
|
hComms(ii, jj) = min([obj.agents{ii}.commsGeometry.radius, obj.agents{jj}.commsGeometry.radius])^2 - norm(agents(ii).pos - agents(jj).pos)^2;
|
|
|
|
A(kk, (3 * ii - 2):(3 * ii)) = 2 * (agents(ii).pos - agents(jj).pos);
|
|
A(kk, (3 * jj - 2):(3 * jj)) = -A(kk, (3 * ii - 2):(3 * ii));
|
|
b(kk) = obj.barrierGain * hComms(ii, jj);
|
|
|
|
% dVNominal = v(ii, 1:3) - v(jj, 1:3); % nominal velocities
|
|
% h_dot_nom = -2 * (agents(ii).pos - agents(jj).pos) * dVNominal';
|
|
% b(kk) = -h_dot_nom + obj.barrierGain * hComms(ii, jj)^3;
|
|
|
|
kk = kk + 1;
|
|
end
|
|
end
|
|
end
|
|
|
|
% Solve QP program generated earlier
|
|
vhat = reshape(v', 3 * size(obj.agents, 1), 1);
|
|
H = 2 * eye(3 * size(obj.agents, 1));
|
|
f = -2 * vhat;
|
|
|
|
% Update solution based on constraints
|
|
assert(size(A,2) == size(H,1))
|
|
assert(size(A,1) == size(b,1))
|
|
assert(size(H,1) == length(f))
|
|
opt = optimoptions('quadprog', 'Display', 'off');
|
|
[vNew, ~, exitflag, m] = quadprog(sparse(H), double(f), A, b, [],[], [], [], [], opt);
|
|
assert(exitflag == 1, sprintf('quadprog failure... %s%s', newline, m.message));
|
|
vNew = reshape(vNew, 3, size(obj.agents, 1))';
|
|
|
|
if exitflag <= 0
|
|
warning("QP failed, continuing with unconstrained solution...")
|
|
vNew = v;
|
|
end
|
|
|
|
% Update the "next position" that was previously set by unconstrained
|
|
% GA using the constrained solution produced here
|
|
for ii = 1:size(vNew, 1)
|
|
obj.agents{ii}.pos = obj.agents{ii}.lastPos + vNew(ii, :) * obj.timestep;
|
|
end
|
|
|
|
% Here we run this at the simulation level, but in reality there is no
|
|
% parent level, so this would be run independently on each agent.
|
|
% Running at the simulation level is just meant to simplify the
|
|
% simulation
|
|
|
|
end |