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