estimateDeltaLie.m

%{
 * Copyright (C) 2013-2025, The Regents of The University of Michigan.
 * All rights reserved.
 * This software was developed in the Biped Lab (https://www.biped.solutions/) 
 * under the direction of Jessy Grizzle, grizzle@umich.edu. This software may 
 * be available under alternative licensing terms; contact the address above.
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer.
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 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS AND
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 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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 * AUTHOR: Bruce JK Huang (bjhuang[at]umich.edu)
 * WEBSITE: https://www.brucerobot.com/
 %}


function [delta, opt]= estimateDeltaLie(opt, data, plane, delta, num_beams, num_targets)
    tic;
    for ring = 1:num_beams
        valid_target_num = num_targets;
        for target = 1:num_targets
            if size(data{target}(ring).points, 2) == 0
                delta(ring).H = eye(4);
                delta(ring).Affine = eye(4);
                valid_target_num = valid_target_num -1;
            end
        end
        
        if valid_target_num < num_targets
            continue
        end
%         ring
%         dbstop in estimateDelta.m at 13 if ring>=32
        theta_x = optimvar('theta_x', 1, 1,'LowerBound',-0.5,'UpperBound',0.5); % 1x1
        theta_y = optimvar('theta_y', 1, 1,'LowerBound',-0.5,'UpperBound',0.5); % 1x1
        theta_z = optimvar('theta_z', 1, 1,'LowerBound',-0.5,'UpperBound',0.5); % 1x1
        T = optimvar('T', 1, 3,'LowerBound', -0.1,'UpperBound',0.1); % 1x3
        S = optimvar('S', 1, 1);

%         theta_x = 0;
%         theta_y = 0;
%         theta_z = 0;
%         S = 1;
%         T = [0 0 0];
%         cost = optimizeMultiIntrinsicCostLie(data, plane, ring, theta_x, theta_y, theta_z, T, S);
                       
        prob = optimproblem;
        f = fcn2optimexpr(@optimizeMultiIntrinsicCostLie, data, plane, ring,...
                           theta_x, theta_y, theta_z, T, S);
        prob.Objective = f;
        x0.theta_x = opt.rpy_init(1);
        x0.theta_y = opt.rpy_init(2);
        x0.theta_z = opt.rpy_init(3);
        x0.S = opt.scale_init;
        x0.T = opt.T_init;

        options = optimoptions('fmincon', 'MaxIter',5e2, 'Display','iter', 'TolX', 1e-6, 'TolFun', 1e-6, 'MaxFunctionEvaluations', 3e4);
        max_trail = 5;
        num_tried = 1;
        status = 0;
        while status <=0 
            [sol, fval, status, ~] = solve(prob, x0, 'Options', options);
            if status <=0 
                warning("optimization failed")
            end
            num_tried = num_tried + 1;
            if (num_tried + 1 > max_trail)
                warning("tried too many time, optimization still failed, current status:")
                disp(status)
                break;
            end
        end
        R_final = rotx(sol.theta_x) * roty(sol.theta_y) * rotz(sol.theta_z);
        delta(ring).H = eye(4);
        delta(ring).H(1:3, 1:3) = R_final;
        delta(ring).H(1:3, 4) = sol.T;
        Scaling = [sol.S    0        0        0
                   0        sol.S    0        0
                   0        0        sol.S    0
                   0        0        0        1];
        delta(ring).Affine = Scaling * delta(ring).H;
        
        delta(ring).opt_total_cost = fval;
        opt.computation_time = toc;
    end
end