74 lines
2.2 KiB
C++
74 lines
2.2 KiB
C++
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/*
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* Copyright (C) 2012 Open Source Robotics Foundation
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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*/
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/* Desc: Simple pendulum motion integrator
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* Author: John Hsu
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* Date: 2012/04/20
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*/
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#include <math.h>
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// integrate d^2 theta / dt^2 = - g * sin(theta) / l
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// by discretizing via central differencing (requires very small dt)
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// (theta_2 - 2*theta_1 + theta_2) / dt^2 = -g * sin(theta_1) / l
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//
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// or euler + 3-4-1 backward Euler is 2nd order:
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//
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// (2*theta_2 - 5*theta_1 + 4*theta_2 -theta_3) / dt^2
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// = -g * sin(theta_1) / l
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//
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// where thata_3 is theta(t - 3*dt)
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// thata_2 is theta(t - 2*dt)
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// thata_1 is theta(t - dt)
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// and
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// thata_f or theta(t_f) is the solution returned
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//
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// If pendulum starts out stationary, one can assume
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// theta_3 = theta_2 = theta_1 = theta_i
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//
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double PendulumAngle(double g, double l, double theta_i,
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double t_i, double t_f , double dt)
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{
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double theta_3 = theta_i;
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double theta_2 = theta_i;
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double theta_1 = theta_i;
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double theta_f = theta_i;
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int steps = ceil((t_f - t_i) / dt);
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double t = t_i;
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for (int i = 0 ; i < steps; i++)
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{
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t += dt;
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theta_f = (-dt*dt*g*sin(theta_1)/l
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+ theta_3
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- 4.0*theta_2
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+ 5.0*theta_1)/2.0;
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/*
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theta_f = (-dt*dt*g*sin(theta_1)/l
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- 1.0*theta_2
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+ 2.0*theta_1);
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*/
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// next step
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theta_3 = theta_2;
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theta_2 = theta_1;
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theta_1 = theta_f;
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// printf("debug t[%f] t_f[%f] theta_f[%f]\n", t, t_f, theta_f);
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}
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if (fabs(t - t_f) > 0.000001)
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printf("time mismatch t[%f] t_f[%f] theta_f[%f]\n", t, t_f, theta_f);
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return theta_f;
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}
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