227 lines
9.9 KiB
Matlab
227 lines
9.9 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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% Compute current velocity and desired control input
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v = zeros(nAgents, 3); % current velocity (for drift term in DI mode)
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u_desired = zeros(nAgents, 3); % desired control: velocity (SI) or acceleration (DI)
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for ii = 1:nAgents
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if obj.useDoubleIntegrator
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v(ii, :) = obj.agents{ii}.lastVel;
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u_desired(ii, :) = (obj.agents{ii}.vel - obj.agents{ii}.lastVel) / obj.timestep;
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else
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v(ii, :) = (obj.agents{ii}.pos - obj.agents{ii}.lastPos) ./ obj.timestep;
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u_desired(ii, :) = v(ii, :);
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end
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end
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if ~obj.useDoubleIntegrator && (all(isnan(v), "all") || all(v == zeros(nAgents, 3), "all"))
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% Single-integrator: agents are not attempting to move
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return;
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end
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if obj.useDoubleIntegrator && all(u_desired == 0, "all") && all(v == 0, "all")
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% Double-integrator: no desired acceleration and no existing velocity
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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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kk = 1;
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A = zeros(obj.numBarriers, 3 * nAgents);
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b = zeros(obj.numBarriers, 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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hMin = -(4 * r_sum_ij * v_max_ij / obj.barrierGain)^(1 / obj.barrierExponent);
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if norm(A(kk, :)) < 1e-9
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% Agents are coincident: A-row is zero, so b < 0 would make
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% 0 ≤ b unsatisfiable. Fall back to b = 0 (no correction possible).
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b(kk) = 0;
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else
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b(kk) = obj.barrierGain * max(hMin, h(ii, jj))^obj.barrierExponent;
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end
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kk = kk + 1;
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end
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end
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idx = length(h(triu(true(size(h)), 1)));
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obj.barriers(1:idx, obj.timestepIndex) = h(triu(true(size(h)), 1));
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idx = idx + 1;
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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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hMin = -(2 * r_i * v_max_i / obj.barrierGain)^(1 / obj.barrierExponent);
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b(kk) = obj.barrierGain * max(hMin, 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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obj.barriers(idx:(idx + numel(hObs) - 1), obj.timestepIndex) = reshape(hObs, [], 1);
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idx = idx + numel(hObs);
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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 — enforce z >= minAlt + radius (not just z >= domain floor + radius)
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h_zMin = (obj.agents{ii}.pos(3) - obj.minAlt) - 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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obj.barriers(idx:(idx + 5), obj.timestepIndex) = [h_xMin; h_xMax; h_yMin; h_yMax; h_zMin; h_zMax];
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idx = idx + 6;
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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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paddingFactor = 0.9; % Barrier at 90% of actual range; real comms still work beyond this
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r_comms = paddingFactor * min([obj.agents{ii}.commsGeometry.radius, obj.agents{jj}.commsGeometry.radius]);
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hComms(ii, jj) = r_comms^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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% One-step forward invariance: b = h/dt ensures h cannot
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% go negative in a single timestep (linear approximation)
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v_max_ij = max(obj.agents{ii}.initialStepSize, obj.agents{jj}.initialStepSize) / obj.timestep;
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hMin = -4 * r_comms * v_max_ij * obj.timestep;
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if norm(A(kk, :)) < 1e-9
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b(kk) = 0;
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else
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b(kk) = max(hMin, hComms(ii, jj)) / obj.timestep;
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end
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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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obj.barriers(idx:(idx + length(hComms(triu(true(size(hComms)), 1))) - 1), obj.timestepIndex) = hComms(triu(true(size(hComms)), 1));
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% Double-integrator: transform QP from velocity to acceleration space.
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% Single-integrator constraint: A * v <= b
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% Double-integrator: A * a <= (b - A * v_current) / dt
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if obj.useDoubleIntegrator
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v_flat = reshape(v', 3 * nAgents, 1);
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b = (b - A * v_flat) / obj.timestep;
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end
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% Solve QP: minimize ||u - u_desired||²
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uhat = reshape(u_desired', 3 * nAgents, 1);
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H = 2 * eye(3 * nAgents);
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f = -2 * uhat;
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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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[uNew, ~, exitflag] = quadprog(H, double(f), A, b, [], [], [], [], x0, opt);
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uNew = reshape(uNew, 3, nAgents)';
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if exitflag < 0
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% Infeasible or other hard failure: hold all agents at current positions
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if coder.target('MATLAB')
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warning("QP infeasible (exitflag=%d), holding positions.", int16(exitflag));
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else
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fprintf("[constrainMotion] QP infeasible (exitflag=%d), holding positions\n", int16(exitflag));
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end
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uNew = zeros(nAgents, 3);
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elseif exitflag == 0
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% Max iterations exceeded: use suboptimal solution already in uNew
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if coder.target('MATLAB')
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warning("QP max iterations exceeded, using suboptimal solution.");
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else
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fprintf("[constrainMotion] QP max iterations exceeded, using suboptimal solution\n");
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end
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end
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% Update agent state using the constrained control input
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for ii = 1:size(uNew, 1)
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if obj.useDoubleIntegrator
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% uNew is constrained acceleration
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obj.agents{ii}.vel = obj.agents{ii}.lastVel + uNew(ii, :) * obj.timestep;
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obj.agents{ii}.pos = obj.agents{ii}.lastPos + obj.agents{ii}.vel * obj.timestep;
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else
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% uNew is constrained velocity
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obj.agents{ii}.pos = obj.agents{ii}.lastPos + uNew(ii, :) * obj.timestep;
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end
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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 |