178 lines
7.4 KiB
Matlab
178 lines
7.4 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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nAgents = size(obj.agents, 1);
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if nAgents < 2
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nAAPairs = 0;
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else
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nAAPairs = nchoosek(nAgents, 2); % unique agent/agent pairs
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end
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% Compute velocity matrix from unconstrained gradient-ascent step
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v = zeros(nAgents, 3);
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for ii = 1:nAgents
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v(ii, :) = (obj.agents{ii}.pos - obj.agents{ii}.lastPos) ./ obj.timestep;
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end
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if all(isnan(v), "all") || all(v == zeros(nAgents, 3), "all")
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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 = nAgents * size(obj.obstacles, 1); % unique agent/obstacle pairs
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nADPairs = nAgents * 6; % agents x (4 walls + 1 floor + 1 ceiling)
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nLNAPairs = sum(obj.constraintAdjacencyMatrix, "all") - nAgents;
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total = nAAPairs + nAOPairs + nADPairs + nLNAPairs;
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kk = 1;
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A = zeros(total, 3 * nAgents);
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b = zeros(total, 1);
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% Set up collision avoidance constraints
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h = NaN(nAgents, nAgents);
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h(logical(eye(nAgents))) = 0; % self value is 0
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for ii = 1:(nAgents - 1)
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for jj = (ii + 1):nAgents
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h(ii, jj) = norm(obj.agents{ii}.pos - obj.agents{jj}.pos)^2 - (obj.agents{ii}.collisionGeometry.radius + obj.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 * (obj.agents{ii}.pos - obj.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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% Slack derived from existing params: recovery velocity = max gradient approach velocity.
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% Correction splits between 2 agents, so |A| = 2*r_sum
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r_sum_ij = obj.agents{ii}.collisionGeometry.radius + obj.agents{jj}.collisionGeometry.radius;
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v_max_ij = max(obj.agents{ii}.initialStepSize, obj.agents{jj}.initialStepSize) / obj.timestep;
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slack = -(4 * r_sum_ij * v_max_ij / obj.barrierGain)^(1 / obj.barrierExponent);
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b(kk) = obj.barrierGain * max(slack, h(ii, jj))^obj.barrierExponent;
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kk = kk + 1;
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end
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end
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hObs = NaN(nAgents, size(obj.obstacles, 1));
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% Set up obstacle avoidance constraints
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for ii = 1:nAgents
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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(obj.agents{ii}.pos);
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hObs(ii, jj) = dot(obj.agents{ii}.pos - cPos, obj.agents{ii}.pos - cPos) - obj.agents{ii}.collisionGeometry.radius^2;
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A(kk, (3 * ii - 2):(3 * ii)) = -2 * (obj.agents{ii}.pos - cPos);
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% Floor for single-agent constraint: full correction on one agent, |A| = 2*r_i
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r_i = obj.agents{ii}.collisionGeometry.radius;
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v_max_i = obj.agents{ii}.initialStepSize / obj.timestep;
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h_floor_i = -(2 * r_i * v_max_i / obj.barrierGain)^(1 / obj.barrierExponent);
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b(kk) = obj.barrierGain * max(h_floor_i, hObs(ii, jj))^obj.barrierExponent;
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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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h_xMin = 0.0; h_xMax = 0.0; h_yMin = 0.0; h_yMax = 0.0; h_zMin = 0.0; h_zMax = 0.0;
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for ii = 1:nAgents
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% X minimum
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h_xMin = (obj.agents{ii}.pos(1) - obj.domain.minCorner(1)) - obj.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 * max(0, h_xMin)^obj.barrierExponent;
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kk = kk + 1;
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% X maximum
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h_xMax = (obj.domain.maxCorner(1) - obj.agents{ii}.pos(1)) - obj.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 * max(0, h_xMax)^obj.barrierExponent;
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kk = kk + 1;
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% Y minimum
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h_yMin = (obj.agents{ii}.pos(2) - obj.domain.minCorner(2)) - obj.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 * max(0, h_yMin)^obj.barrierExponent;
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kk = kk + 1;
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% Y maximum
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h_yMax = (obj.domain.maxCorner(2) - obj.agents{ii}.pos(2)) - obj.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 * max(0, h_yMax)^obj.barrierExponent;
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kk = kk + 1;
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% Z minimum
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h_zMin = (obj.agents{ii}.pos(3) - obj.domain.minCorner(3)) - obj.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 * max(0, h_zMin)^obj.barrierExponent;
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kk = kk + 1;
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% Z maximum
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h_zMax = (obj.domain.maxCorner(3) - obj.agents{ii}.pos(3)) - obj.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 * max(0, h_zMax)^obj.barrierExponent;
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kk = kk + 1;
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end
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if coder.target('MATLAB')
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% Save off h function values (logging only — not needed in compiled mode)
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obj.h(:, obj.timestepIndex) = [h(triu(true(nAgents), 1)); reshape(hObs, [], 1); h_xMin; h_xMax; h_yMin; h_yMax; h_zMin; h_zMax;];
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end
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% Add communication network constraints
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hComms = NaN(nAgents, nAgents);
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hComms(logical(eye(nAgents))) = 0;
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for ii = 1:(nAgents - 1)
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for jj = (ii + 1):nAgents
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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(obj.agents{ii}.pos - obj.agents{jj}.pos)^2;
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A(kk, (3 * ii - 2):(3 * ii)) = 2 * (obj.agents{ii}.pos - obj.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 * max(0, hComms(ii, jj))^obj.barrierExponent;
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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 * nAgents, 1);
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H = 2 * eye(3 * nAgents);
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f = -2 * vhat;
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% Update solution based on constraints
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if coder.target('MATLAB')
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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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end
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opt = optimoptions("quadprog", "Display", "off", "Algorithm", "active-set", "UseCodegenSolver", true);
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x0 = zeros(size(H, 1), 1);
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[vNew, ~, exitflag, m] = quadprog(H, double(f), A, b, [], [], [], [], x0, opt);
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if coder.target('MATLAB')
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assert(exitflag == 1, sprintf("quadprog failure... %s%s", newline, m.message));
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end
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vNew = reshape(vNew, 3, nAgents)';
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if exitflag <= 0
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if coder.target('MATLAB')
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warning("QP failed, continuing with unconstrained solution...")
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end
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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 |