Commit 08324921 authored by Hendrik Geisler's avatar Hendrik Geisler

Full motion cycle w/o damping

parent f2798331
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......@@ -7,7 +7,7 @@ public:
static constexpr double eta = 0.7; //!< coefficient of restitution
static constexpr double epsilon = 0.05; //!< distance to ground to apply friction, numerically motivated
static constexpr double mu_static = 0.9; //!< static friction coefficient
static constexpr double mu_kinetic = 0.68; //0.68; //!< kinetic friction coefficient (sliding)
static constexpr double mu_kinetic = 0; // 0.68; //0.68; //!< kinetic friction coefficient (sliding)
//static
......
......@@ -5,11 +5,13 @@
DER::DER() {
this->prob = NULL;
this->s0 = NULL; //Not needed
F = MatrixXd::Zero(4 * NUM_N, 1);
}
DER::DER(Problem* prob) {
this->prob = prob;
this->s0 = NULL; //Not needed
F = MatrixXd::Zero(4 * NUM_N, 1);
}
DER::DER(Problem* prob, VectorXd* s0) {
......@@ -230,7 +232,7 @@ void DER::operator() (const state_type& s, state_type& ds, const double t) {
F_int_vec.block(0, 0, 2 * N, 1) = (Map<VectorXd>(F_int.data(), F_int.size()));
F_int_vec.block(2*N, 0, 2 * N, 1) = (Map<VectorXd>(P_int.data(), P_int.size()));
VectorXd F_damp(4 * N);
F_damp = - prob->Damp * dq; //Numerical Damping //0.00001
F_damp = - 0 * dq; //Numerical Damping //0.00001
if (prob->Damp > 1000) {
std::cout << "b";
......
......@@ -12,9 +12,9 @@
using namespace Eigen;
constexpr int NUM_N = 30;
constexpr int NUM_N_LEFT = 10;
constexpr int NUM_N_RIGHT = 10;
constexpr int NUM_N = 40;
constexpr int NUM_N_LEFT = 12;
constexpr int NUM_N_RIGHT = 12;
/*!
* Set up the Problem using a Cross Section, a Material and the Configuration.
......
......@@ -38,16 +38,19 @@ void RobotExact::setLeftCurvature(state_type& x, double left, double part, direc
upperConfigX = x.block(0, 0, 2 * NUM_N, 1); //Save the upper configuration
lowerConfigX = VectorXd::Zero(2 * NUM_N);
state_type initX = x;
state_type initX = Prob->s0;
std::cout << "_________________________________" << std::endl;
RobotApprox* robApprox = new RobotApprox(this->System, this->Prob);
DER* System = new DER(this->Prob);
RobotApprox* robApprox = new RobotApprox(System, this->Prob);
Simulator sim2 = Simulator(robApprox, this->Prob);
sim2.startSimLeftDownApprox(initX);
sim2.startSimLeftDownApprox(initX); //Laying on the ground
std::cout << "_________________________________" << std::endl;
lowerConfigX = sim2.x_vec[sim2.x_vec.size() - 1].block(0, 0, 2 * NUM_N, 1);
//lowerConfigX = Prob->s0.block(0, 0, 2 * NUM_N, 1);;
delete System;
delete robApprox;
//std::cout << lowerConfigX << std::endl;
......@@ -58,11 +61,39 @@ void RobotExact::setLeftCurvature(state_type& x, double left, double part, direc
lowerConfigX(2 * i + 1) = lowerConfigX(2 * i + 1) - dx + upperConfigX(1);
lowerConfigX(2 * i) = lowerConfigX(2 * i) - dy;
}
std::cout << dx << dy << std::endl;
std::cout << lowerConfigX << std::endl;
configSaved = true;
std::cout << "Lower Configuration calculated" << std::endl;
}
state_type xCopy = x;
//Now give the appropriate BC
if (abs(System->F(1) / System->F(0)) > Contact::mu_static) { //Slip
setLeftCurvatureSlip(x, left, part); //Sliping
//Friction Forces, (only lowest node is in contact)
if (abs(x(4 * NUM_N + 1)) > 0) {
Prob->fricForces(1) = -x(4 * NUM_N + 1) / abs(x(4 * NUM_N + 1)) * Contact::mu_kinetic * System->F(1);
}
else {
Prob->fricForces(1) = 0;
}
}
else {
setLeftCurvatureStick(x, left, part); //Sticking
}
//Now test
for (int i = 0; i < NUM_N; i++) {
if (x(2 * i) <= lowerConfigX(2 * i)) {
x(2*i) = xCopy(2*i); //Don't change;
}
}
if (part == 1.0) {
x.block(0, 0, 2*NUM_N, 0) = lowerConfigX;
}
//Now give the appropriate BC
for (int i = 0; i < 2 * NUM_N_LEFT; i = i + 2) {
x(i) = (1.0 - part) * lowerConfigX(i) + part * upperConfigX(i);
......
......@@ -171,6 +171,11 @@ void RobotVirtual::setRightCurvature(state_type& x, double right, double part, d
//Nothing.
}
for (int i = 0; i < 2 * NUM_N_LEFT; i = i + 2) {
x(4 * NUM_N + i) = 0;
x(4 * NUM_N + i + 1) = 0;
}
}
else {
if (abs(System->F(2 * NUM_N - 1) / System->F(2 * NUM_N - 2)) > Contact::mu_static) { //Slip
......@@ -186,6 +191,10 @@ void RobotVirtual::setRightCurvature(state_type& x, double right, double part, d
else {
setRightCurvatureStick(x, right, part); //Sticking
}
for (int i = 0; i < 2 * NUM_N_LEFT; i = i + 2) {
x(4 * NUM_N + i) = 0;
x(4 * NUM_N + i + 1) = 0;
}
}
}
......@@ -212,7 +221,7 @@ void RobotVirtual::setRightCurvatureSlip(state_type& x, double right, double par
alpha += alpha_r;
}
double dx = 0; // x_end - x(2 * NUM_N - 1);
double dx = 0; // x_end - x(2 * NUM_N - 1); //0
double dy = y_end - x(2 * NUM_N - 2);
//Move whole arm, that last bottom node does not move
......
......@@ -45,7 +45,6 @@ void Simulator::startSimComplete() {
setCurvature(t, x);
controlBC(x);
setBC(t);
groundCheck(x);
pushBackState(t, dt, x);
}
......@@ -66,7 +65,7 @@ void Simulator::startSimLeftDownApprox(state_type& x) {
//Solving the system with odeint
error_stepper_type::time_type t = 2.0;
error_stepper_type::time_type dt = 0.001;
t_max = 6.0;
t_max = 3.0;
auto start = std::chrono::high_resolution_clock::now();
auto stepper = make_controlled<error_stepper_type>(1.0e-5, 1.0e-5);
......@@ -81,47 +80,16 @@ void Simulator::startSimLeftDownApprox(state_type& x) {
stepper.try_step(*Crawler, x, t, dt);
if (t >= 2.0) {
partLeft = RobotVirtual::rampStepDown(2.0, 0.5, 6.0, t);
partRight = 1.0; //To ensure we are at the correct position
partLeft = 0.0; //RobotVirtual::rampStepDown(2.0, 0.5, 6.0, t);
partRight = RobotVirtual::rampStepUp(2.0, 0.5, 6.0, t);
lDir = down;
}
Crawler->setRightCurvature(x, -0.1, partRight, rDir);
Crawler->setLeftCurvature(x, -0.1, partLeft, lDir);
Crawler->setRightCurvature(x, -0.3, partRight, rDir);
Crawler->setLeftCurvature(x, -0.3, partLeft, lDir);
controlBC(x);
if (2.49 < t && t < 3.0) {
//std::cout << "Hey ho" << std::endl;
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.01; // *(pow(4.5 - t, 3));
}
else if (3.0 < t && t <= 4) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.0001;
}
else if (4.0 < t && t <= 5) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.00001;
}
else if (5.0 < t && t <= 6) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.0000000000;
}
/*else if (4.5 < t && t <= 6) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.0;
}*/
else {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0;
}
controlBC(x);
groundCheck(x);
if (fmod(step, 500) == 0) {
......@@ -179,6 +147,22 @@ void Simulator::startSimLeftDownApprox(state_type& x) {
void Simulator::setCurvature(const double &t, state_type &x) {
//Start Motion
/*partLeft = RobotVirtual::rampStepUp(1.0, 0.5, 2.0, t);
lDir = up;
partRight = RobotVirtual::rampStepUp(0.0, 0.5, 2.0, t);
rDir = up;*/
/*if (t < 1.0) {
partRight = RobotVirtual::rampStepUp(0.0, 0.5, 2.0, t);
lDir = up;
partLeft = RobotVirtual::rampStepUp(6.0, 0.5, 8.0, t);
rDir = up;
}
if (t >= 1.0) {
partRight = RobotVirtual::rampStepDown(1.0, 0.5, 6.0, t);
lDir = down;
partLeft = RobotVirtual::rampStepUp(6.0, 0.5, 8.0, t);
rDir = up;
}*/
if (t < 2.0) {
partLeft = RobotVirtual::rampStepUp(0.0, 0.5, 2.0, t);
lDir = up;
......@@ -192,8 +176,11 @@ void Simulator::setCurvature(const double &t, state_type &x) {
rDir = down;
}
Crawler->setRightCurvature(x, -0.1, partRight, rDir);
Crawler->setLeftCurvature(x, -0.1, partLeft, lDir);
Crawler->setRightCurvature(x, -0.3, partRight, rDir);
Crawler->setLeftCurvature(x, -0.3, partLeft, lDir);
}
void Simulator::pushBackState(double &t, const double &dt, state_type &x) {
......@@ -225,42 +212,6 @@ void Simulator::groundCheck(state_type &x) {
step++;
}
void Simulator::setBC(const double &t) {
if (2.5 < t && t < 3.0) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.0;
} else if (3.0 < t && t <= 4.0) {
Prob->boundaryConditions(0) = 1;
Prob->boundaryConditions(1) = 1;
Prob->Damp = 0.0;
//Prob->boundaryConditions(2*NUM_N - 2) = 1;
//Prob->boundaryConditions(2*NUM_N - 1) = 1;
}
//if (2.49 < t && t < 3.00) {
// //std::cout << "Hey ho" << std::endl;
// Prob->boundaryConditions(0) = 0;
// Prob->boundaryConditions(1) = 0;
// Prob->Damp = 0.01;
//}
//else if (3.0 < t && t <= 3.5) {
// Prob->boundaryConditions(0) = 1;
// Prob->boundaryConditions(1) = 0;
// Prob->Damp = 0.0001;
//}
//else if (3.5 < t && t <= 6) {
// Prob->boundaryConditions(0) = 0;
// Prob->boundaryConditions(1) = 0;
// Prob->Damp = 0.0;
//}
//else {
// Prob->boundaryConditions(0) = 1;
// Prob->boundaryConditions(1) = 1;
// Prob->Damp = 0;
//}
}
void Simulator::controlBC(state_type& x) {
//If nodes are controlled via boundary conditions, do not let DER change them
for (int i = 0; i < 2 * NUM_N_LEFT; i = i + 2) {
......@@ -283,7 +234,7 @@ void Simulator::controlBC(state_type& x) {
}
//if part == 0 check sticking for DER Formulation. Nodes in contact should not move, if sticking
if (partLeft <= 1E-8) {
if (partLeft <= 1E-6) {
for (int i = 0; i < 2 * NUM_N_LEFT; i = i + 2) {
//Control Sticking: (only useful if no curvature set):
if (x(i) <= -height) {
......@@ -305,7 +256,7 @@ void Simulator::controlBC(state_type& x) {
}
}
if (partRight <= 1E-8) {
if (partRight <= 1E-6) {
for (int i = 2 * NUM_N; i > 2 * (NUM_N - NUM_N_RIGHT); i = i - 2) {
//Control Sticking: (only useful if no curvature set):
if (x(i) <= -height) {
......
......@@ -34,7 +34,6 @@ public:
void setCurvature(const double &t, state_type &x);
void pushBackState(double &t, const double &dt, state_type &x);
void groundCheck(state_type &x);
void setBC(const double &t);
void controlBC(state_type&);
void writeCSV();
......
......@@ -43,11 +43,11 @@ axis([0 4 -4 4]);
f = readmatrix("../f.csv");
f = f(1:end, 1:end-1);
figure
plot(t', f(:, 39), 'Linewidth', 3);
plot(t', f(:, 79), 'Linewidth', 3);
hold on
plot(t', f(:, 40), 'Linewidth', 3);
CF = abs(f(:, 40)./f(:, 39));
CF(CF>2) = 2;
plot(t', f(:, 80), 'Linewidth', 3);
CF = abs(f(:, 80)./f(:, 79));
%CF(CF>2) = 2;
plot(t', CF, 'Linewidth', 3);
legend('E2', 'E3', 'Friction');
set(gca,'FontSize', 26);
......
......@@ -25,7 +25,7 @@ set(gca,'FontSize', 26);
colorbar
%%
f = readmatrix("../f.csv");
f = readmatrix("../f1.csv");
f = f(1:end, 1:end-1);
figure
plot(t', f(:, 1), 'Linewidth', 3);
......@@ -36,7 +36,7 @@ CF = abs(f(:, 2)./f(:, 1));
plot(t', CF, 'Linewidth', 3);
legend('E2', 'E3', 'Friction');
set(gca,'FontSize', 26);
axis([0 4 -4 4]);
%axis([0 4 -4 4]);
%%
%%
......
eN = 10;
figure;
for j = 255
for j = 53:102
x_all = [];
for i = 1:30
for i = 1:40
x_all = [x_all, [x(j, 2*i-1); x(j, 2*i)]];
end
x_all(2, 1:30) = x_all(2, 1:30) - x_all(2, 1);
plot(x_all(2, 1:30), x_all(1, 1:30), 'Color', [17 17 200]/255, 'Linewidth', 3);
x_all(2, 1:40) = x_all(2, 1:40) - x_all(2, 1);
plot(x_all(2, 1:40), x_all(1, 1:40), 'Color', [17 17 200]/255, 'Linewidth', 3);
hold on
end
......
......@@ -2,7 +2,7 @@
Table tableT;
int NUM_N;
int moveX = 600;
int moveX = 400;
int scaleX = 3000;
int moveY = 400;
int scaleY = 3000;
......
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\ No newline at end of file
This diff is collapsed.
0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.11,0.12,0.13,0.14,0.15,0.16,0.17,0.18,0.19,0.2,0.21,0.22,0.23,0.24,0.25,0.26,0.27,0.28,0.29,0.3,0.31,0.32,0.33,0.34,0.35,0.36,0.37,0.38,0.39,0.4,0.41,0.42,0.43,0.44,0.45,0.46,0.47,0.48,0.49,0.5,0.51,0.52,0.53,0.54,0.55,0.56,0.57,0.58,0.59,0.6,0.61,0.62,0.63,0.64,0.65,0.66,0.67,0.68,0.69,0.7,0.71,0.72,0.73,0.74,0.75,0.76,0.77,0.78,0.79,0.8,0.81,0.82,0.83,0.84,0.85,0.86,0.87,0.88,0.89,0.9,0.91,0.92,0.93,0.94,0.95,0.96,0.97,0.98,0.99,1,1.01,1.02,1.03,1.04,1.05,1.06,1.07,1.08,1.09,1.1,1.11,1.12,1.13,1.14,1.15,1.16,1.17,1.18,1.19,1.2,1.21,1.22,1.23,1.24,1.25,1.26,1.27,1.28,1.29,1.3,1.31,1.32,1.33,1.34,1.35,1.36,1.37,1.38,1.39,1.4,1.41,1.42,1.43,1.44,1.45,1.46,1.47,1.48,1.49,1.5,1.51,1.52,1.53,1.54,1.55,1.56,1.57,1.58,1.59,1.6,1.61,1.62,1.63,1.64,1.65,1.66,1.67,1.68,1.69,1.7,1.71,1.72,1.73,1.74,1.75,1.76,1.77,1.78,1.79,1.8,1.81,1.82,1.83,1.84,1.85,1.86,1.87,1.88,1.89,1.9,1.91,1.92,1.93,1.94,1.95,1.96,1.97,1.98,1.99,2,2.01,2.02,2.03,2.04,2.05,2.06,2.07,2.08,2.09,2.1,2.11,2.12,2.13,2.14,2.15,2.16,2.17,2.18,2.19,2.2,2.21,2.22,2.23,2.24,2.25,2.26,2.27,2.28,2.29,2.3,2.31,2.32,2.33,2.33844,2.34724,2.35603,2.3646,2.3731,2.3816,2.39002,2.39745,2.40538,2.41296,2.41994,2.42722,2.43449,2.44176,2.44904,2.45618,2.46338,2.47069,2.47801,2.48532,2.49275,2.50031,2.50787,2.51485,2.52234,2.53,2.53782,2.54527,2.55316,2.5605,2.56843,2.57654,2.58423,2.59113,2.59814,2.60515,2.61216,2.61937,2.62686,2.63453,2.64228,2.65009,2.65851,2.66739,2.67604,2.68402,2.69211,2.70053,2.70916,2.71798,2.72679,2.73579,2.74552,2.75552,2.76552,2.7753,2.78436,2.79373,2.80358,2.81342,2.82326,2.83324,2.84324,2.85324,2.86324,2.87324,2.88324,2.89324,2.90324,2.91324,2.92324,2.93324,2.94286,2.95185,2.96085,2.96984,2.97751,2.98562,2.99372,3.00183,3.00994,3.01805,3.02596,3.03357,3.04118,3.04879,3.05641,3.06402,3.07163,3.07924,3.08706,3.09493,3.1028,3.11067,3.11854,3.12641,3.13428,3.14221,3.15023,3.15864,3.16741,3.17647,3.18573,3.19511,3.20453,3.21435,3.22435,3.23435,3.24435,3.25435,3.26435,3.27435,3.28435,3.29435,3.30435,3.31435,3.32435,3.33435,3.34435,3.35435,3.36435,3.37435,3.38435,3.39435,3.40435,3.41435,3.42435,3.43435,3.44435,3.45435,3.46435,3.47435,3.48435,3.49435,3.50435,3.51435,3.52435,3.53435,3.54435,3.55435,3.56435,3.57435,3.58435,3.59435,3.60435,3.61435,3.62435,3.63435,3.64435,3.65435,3.66435,3.67435,3.68435,3.69435,3.70435,3.71435,3.72435,3.73435,3.74435,3.75435,3.76435,3.77435,3.78435,3.79435,3.80435,3.81435,3.82435,3.83435,3.84435,3.85435,3.86435,3.87435,3.88435,3.89435,3.90435,3.91435,3.92435,3.93435,3.94435,3.95435,3.96435,3.97435,3.98435,3.99435,
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# Overview
## 1. Implementation with k1, k3, k4
## Theory
### DER
Bergou
Evans Theory
assumptions to our form of the theory
experiments + comparison to analytic solutions
### Soft robotics
Motivation
Robot from Harvard for Locomotion
#### Actuation
Pneumatics
Modelling
Pictures of actuator
## Simulation Locomotion
### 1. Implementation with k1, k3, k4
Benchmark using the Intel Compiler
Comparison between MSVC Compiler and Intel Compiler
## 2. Real Problem
### 2. Real Problem
E, I smaller; damping 0.00001 is enough
Calibration (coordinate descent method)
k3, k4, k5 with crosssection angle instead of delta_3
k1 = 2; k3 = 0.2; k4 = 0.02; k5 = 0.4;
## 3. Boundary Condition to give curvature
### 3. Boundary Condition to give curvature
Curvature constant, compare to Olivers Paper on modelling actuators (not entirely correct)
Hugh forces against small I -> okay
Only prescribe x. Let D be calculated by DER.
......@@ -21,35 +41,34 @@ Only prescribe x. Let D be calculated by DER.
1. Left up: Trivial, 0 curvature to part of circle
2. Right up: Initial curvature given. Do not change curvature until reached initial curvature.
3. Left down: Part of circle to sigmoid function (no slip)
3. Left down:
Predictor - Corrector:
Part of circle to sigmoid function (no slip)
$s = 0.03 * \frac{1.}{(1 + exp(-b*t))}$
$h = \sum_{i = 1}^{N} delL * sin(\alpha * i)$
4. Right down: Trivial, no curvature at end.
### 3
Can calculate end position, if we ignore some BC.
For different angles of the right side, we find the height of the end node of the left arm and fit a quadratic parabola:
| angle | p(2) | p(1) | p(0) | |
|------ |--- |--- |--- |--- |
| | | | | |
| | | | | |
| | | | | |
No good fit for all angles found. Want robust solution
## 4. Stick/Slip motion
### 4. Stick/Slip motion
Slip: two dir possible. Physical Reasoning needed.
Static, dynamic friction
Slip: two dir possible. Physical Reasoning needed.
Static, dynamic friction