Diff: Motion.cpp

Revision:

3:e6d345973797

Child:

4:52d2d31a7347

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Motion.cpp	Thu Dec 05 09:02:14 2019 +0000
@@ -0,0 +1,778 @@
+/*
+ * Motion.cpp
+ * Copyright (c) 2017, ZHAW
+ * All rights reserved.
+ *
+ *  Created on: 02.02.2017
+ *      Author: Marcel Honegger
+ */
+
+#include <cmath>
+#include <algorithm>
+#include "Motion.h"
+
+const float Motion::DEFAULT_LIMIT = 1.0f;       // default value for limits
+const float Motion::MINIMUM_LIMIT = 1.0e-6f;    // smallest value allowed for limits
+
+/**
+ * Creates a <code>Motion</code> object.
+ * The values for position, velocity and acceleration are set to 0.
+ */
+Motion::Motion() {
+
+  position      = 0.0;
+  velocity      = 0.0f;
+  acceleration  = 0.0f;
+
+  profileVelocity     = DEFAULT_LIMIT;
+  profileAcceleration = DEFAULT_LIMIT;
+  profileDeceleration = DEFAULT_LIMIT;
+}
+
+/**
+ * Creates a <code>Motion</code> object with given values for position and velocity.
+ * @param position the initial position value of this motion, given in [m] or [rad].
+ * @param velocity the initial velocity value of this motion, given in [m/s] or [rad/s].
+ */
+Motion::Motion(double position, float velocity) {
+
+  this->position      = position;
+  this->velocity      = velocity;
+  this->acceleration  = 0.0f;
+
+  profileVelocity     = DEFAULT_LIMIT;
+  profileAcceleration = DEFAULT_LIMIT;
+  profileDeceleration = DEFAULT_LIMIT;
+}
+
+/**
+ * Creates a <code>Motion</code> object with given values for position, velocity and acceleration.
+ * @param position the initial position value of this motion, given in [m] or [rad].
+ * @param velocity the initial velocity value of this motion, given in [m/s] or [rad/s].
+ * @param acceleration the initial acceleration value of this motion, given in [m/s&sup2;] or [rad/s&sup2;].
+ */
+Motion::Motion(double position, float velocity, float acceleration) {
+
+  this->position      = position;
+  this->velocity      = velocity;
+  this->acceleration  = acceleration;
+
+  profileVelocity     = DEFAULT_LIMIT;
+  profileAcceleration = DEFAULT_LIMIT;
+  profileDeceleration = DEFAULT_LIMIT;
+}
+
+/**
+ * Creates a <code>Motion</code> object with given values for position, velocity and acceleration.
+ * @param position the initial position value of this motion, given in [m] or [rad].
+ * @param velocity the initial velocity value of this motion, given in [m/s] or [rad/s].
+ * @param profileVelocity the limit of the velocity.
+ * @param profileAcceleration the limit of the acceleration.
+ * @param profileDeceleration equal to profileAcceleration.
+ */
+Motion::Motion(double position, float velocity, float profileVelocity, float profileAcceleration) {
+
+  this->position      = position;
+  this->velocity      = velocity;
+  this->acceleration  = 0.0f;
+
+  this->profileVelocity     = profileVelocity;
+  this->profileAcceleration = profileAcceleration;
+  this->profileDeceleration = profileAcceleration;
+}
+
+/**
+ * Creates a <code>Motion</code> object with given values for position and velocity.
+ * @param motion another <code>Motion</code> object to copy the values from.
+ */
+Motion::Motion(const Motion& motion) {
+
+  position      = motion.position;
+  velocity      = motion.velocity;
+  acceleration  = motion.acceleration;
+
+  profileVelocity     = motion.profileVelocity;
+  profileAcceleration = motion.profileAcceleration;
+  profileDeceleration = motion.profileDeceleration;
+}
+
+Motion::~Motion() {}
+
+/**
+ * Sets the values for position and velocity.
+ * @param position the desired position value of this motion, given in [m] or [rad].
+ * @param velocity the desired velocity value of this motion, given in [m/s] or [rad/s].
+ */
+void Motion::set(double position, float velocity) {
+
+  this->position = position;
+  this->velocity = velocity;
+}
+
+/**
+ * Sets the values for position, velocity and acceleration.
+ * @param position the desired position value of this motion, given in [m] or [rad].
+ * @param velocity the desired velocity value of this motion, given in [m/s] or [rad/s].
+ * @param acceleration the desired acceleration value of this motion, given in [m/s&sup2;] or [rad/s&sup2;].
+ */
+void Motion::set(double position, float velocity, float acceleration) {
+
+  this->position      = position;
+  this->velocity      = velocity;
+  this->acceleration  = acceleration;
+}
+
+/**
+ * Sets the values for position, velocity and acceleration.
+ * @param motion another <code>Motion</code> object to copy the values from.
+ */
+void Motion::set(const Motion& motion) {
+
+  position      = motion.position;
+  velocity      = motion.velocity;
+  acceleration  = motion.acceleration;
+}
+
+/**
+ * Sets the position value.
+ * @param position the desired position value of this motion, given in [m] or [rad].
+ */
+void Motion::setPosition(double position) {
+
+  this->position = position;
+}
+
+/**
+ * Gets the position value.
+ * @return the position value of this motion, given in [m] or [rad].
+ */
+double Motion::getPosition() {
+
+  return position;
+}
+
+/**
+ * Sets the velocity value.
+ * @param velocity the desired velocity value of this motion, given in [m/s] or [rad/s].
+ */
+void Motion::setVelocity(float velocity) {
+
+  this->velocity = velocity;
+}
+
+/**
+ * Gets the velocity value.
+ * @return the velocity value of this motion, given in [m/s] or [rad/s].
+ */
+float Motion::getVelocity() {
+
+  return velocity;
+}
+
+/**
+ * Sets the acceleration value.
+ * @param acceleration the desired acceleration value of this motion, given in [m/s&sup2;] or [rad/s&sup2;].
+ */
+void Motion::setAcceleration(float acceleration) {
+
+  this->acceleration = acceleration;
+}
+
+/**
+ * Gets the acceleration value.
+ * @return the acceleration value of this motion, given in [m/s&sup2;] or [rad/s&sup2;].
+ */
+float Motion::getAcceleration() {
+
+  return acceleration;
+}
+
+/**
+ * Sets the limit for the velocity value.
+ * @param profileVelocity the limit of the velocity.
+ */
+void Motion::setProfileVelocity(float profileVelocity) {
+
+  if (profileVelocity > MINIMUM_LIMIT) this->profileVelocity = profileVelocity; else this->profileVelocity = MINIMUM_LIMIT;
+}
+
+/**
+ * Sets the limit for the acceleration value.
+ * @param profileAcceleration the limit of the acceleration.
+ */
+void Motion::setProfileAcceleration(float profileAcceleration) {
+
+  if (profileAcceleration > MINIMUM_LIMIT) this->profileAcceleration = profileAcceleration; else this->profileAcceleration = MINIMUM_LIMIT;
+}
+
+/**
+ * Sets the limit for the deceleration value.
+ * @param profileDeceleration the limit of the deceleration.
+ */
+void Motion::setProfileDeceleration(float profileDeceleration) {
+
+  if (profileDeceleration > MINIMUM_LIMIT) this->profileDeceleration = profileDeceleration; else this->profileDeceleration = MINIMUM_LIMIT;
+}
+
+/**
+ * Sets the limits for velocity, acceleration and deceleration values.
+ * @param profileVelocity the limit of the velocity.
+ * @param profileAcceleration the limit of the acceleration.
+ * @param profileDeceleration the limit of the deceleration.
+ */
+void Motion::setLimits(float profileVelocity, float profileAcceleration, float profileDeceleration) {
+
+  if (profileVelocity > MINIMUM_LIMIT) this->profileVelocity = profileVelocity; else this->profileVelocity = MINIMUM_LIMIT;
+  if (profileAcceleration > MINIMUM_LIMIT) this->profileAcceleration = profileAcceleration; else this->profileAcceleration = MINIMUM_LIMIT;
+  if (profileDeceleration > MINIMUM_LIMIT) this->profileDeceleration = profileDeceleration; else this->profileDeceleration = MINIMUM_LIMIT;
+}
+
+/**
+ * Gets the time needed to move to a given target position.
+ * @param targetPosition the desired target position given in [m] or [rad].
+ * @return the time to move to the target position, given in [s].
+ */
+float Motion::getTimeToPosition(double targetPosition) {
+
+  // calculate position, when velocity is reduced to zero
+
+  double stopPosition = (velocity > 0.0f) ? position+static_cast<double>(velocity*velocity/profileDeceleration*0.5f) : position-static_cast<double>(velocity*velocity/profileDeceleration*0.5f);
+
+  if (targetPosition > stopPosition) { // positive velocity required
+
+    if (velocity > profileVelocity) { // slow down to profile velocity first
+
+      float t1 = (velocity-profileVelocity)/profileDeceleration;
+      float t2 = static_cast<float>(targetPosition-stopPosition)/profileVelocity;
+      float t3 = profileVelocity/profileDeceleration;
+
+      return t1+t2+t3;
+
+    } else if (velocity > 0.0f) { // speed up to profile velocity
+
+      float t1 = (profileVelocity-velocity)/profileAcceleration;
+      float t3 = profileVelocity/profileDeceleration;
+      float t2 = (static_cast<float>(targetPosition-position)-(velocity+profileVelocity)*0.5f*t1)/profileVelocity-0.5f*t3;
+
+      if (t2 < 0.0f) {
+        float maxVelocity = std::sqrt((2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+        t1 = (maxVelocity-velocity)/profileAcceleration;
+        t2 = 0.0f;
+        t3 = maxVelocity/profileDeceleration;
+      }
+
+      return t1+t2+t3;
+
+    } else { // slow down to zero first, and then speed up to profile velocity
+
+      float t1 = -velocity/profileDeceleration;
+      float t2 = profileVelocity/profileAcceleration;
+      float t4 = profileVelocity/profileDeceleration;
+      float t3 = (static_cast<float>(targetPosition-position)-velocity*0.5f*t1)/profileVelocity-0.5f*(t2+t4);
+
+      if (t3 < 0.0f) {
+        float maxVelocity = std::sqrt((2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+        t2 = maxVelocity/profileAcceleration;
+        t3 = 0.0f;
+        t4 = maxVelocity/profileDeceleration;
+      }
+
+      return t1+t2+t3+t4;
+    }
+
+  } else { // negative velocity required
+
+    if (velocity < -profileVelocity) { // slow down to (negative) profile velocity first
+
+      float t1 = (-profileVelocity-velocity)/profileDeceleration;
+      float t2 = static_cast<float>(stopPosition-targetPosition)/profileVelocity;
+      float t3 = profileVelocity/profileDeceleration;
+
+      return t1+t2+t3;
+
+    } else if (velocity < 0.0f) { // speed up to (negative) profile velocity
+
+      float t1 = (velocity+profileVelocity)/profileAcceleration;
+      float t3 = profileVelocity/profileDeceleration;
+      float t2 = (static_cast<float>(position-targetPosition)+(velocity-profileVelocity)*0.5f*t1)/profileVelocity-0.5f*t3;
+
+      if (t2 < 0.0f) {
+        float minVelocity = -std::sqrt((-2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+        t1 = (velocity-minVelocity)/profileAcceleration;
+        t2 = 0.0f;
+        t3 = -minVelocity/profileDeceleration;
+      }
+
+      return t1+t2+t3;
+
+    } else { // slow down to zero first, and then speed up to (negative) profile velocity
+
+      float t1 = velocity/profileDeceleration;
+      float t2 = profileVelocity/profileAcceleration;
+      float t4 = profileVelocity/profileDeceleration;
+      float t3 = (-static_cast<float>(targetPosition-position)+velocity*0.5f*t1)/profileVelocity-0.5f*(t2+t4);
+
+      if (t3 < 0.0f) {
+        float minVelocity = -std::sqrt((-2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+        t2 = -minVelocity/profileAcceleration;
+        t3 = 0.0f;
+        t4 = -minVelocity/profileDeceleration;
+      }
+
+      return t1+t2+t3+t4;
+    }
+  }
+}
+
+/**
+ * Gets the distance moved until the velocity reaches zero.
+ * @return the distance to the stop position.
+ */
+double Motion::getDistanceToStop() {
+
+  return static_cast<double>(velocity*velocity/profileDeceleration*0.5f);
+}
+
+/**
+ * Increments the current motion towards a given target velocity.
+ * @param targetVelocity the desired target velocity given in [m/s] or [rad/s].
+ * @param period the time period to increment the motion values for, given in [s].
+ */
+void Motion::incrementToVelocity(float targetVelocity, float period) {
+
+  if (targetVelocity < -profileVelocity) targetVelocity = -profileVelocity;
+  else if (targetVelocity > profileVelocity) targetVelocity = profileVelocity;
+
+  if (targetVelocity > 0.0f) {
+
+    if (velocity > targetVelocity) { // slow down to target velocity
+
+      float t1 = (velocity-targetVelocity)/profileDeceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*period)*period);
+        velocity += -profileDeceleration*period;
+        acceleration = -profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      }
+
+    } else if (velocity > 0.0f) { // speed up to target velocity
+
+      float t1 = (targetVelocity-velocity)/profileAcceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*period)*period);
+        velocity += profileAcceleration*period;
+        acceleration = profileAcceleration;
+      } else {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t1)*t1);
+        velocity += profileAcceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      }
+
+    } else { // slow down to zero first, and then speed up to target velocity
+
+      float t1 = -velocity/profileDeceleration;
+      float t2 = targetVelocity/profileAcceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*period)*period);
+        velocity += profileDeceleration*period;
+        acceleration = profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*(period-t1))*(period-t1));
+        velocity += profileAcceleration*(period-t1);
+        acceleration = profileAcceleration;
+      } else {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t2)*t2);
+        velocity += profileAcceleration*t2;
+        position += static_cast<double>(velocity*(period-t1-t2));
+        acceleration = 0.0f;
+      }
+    }
+
+  } else {
+
+    if (velocity < targetVelocity) { // slow down to (negative) target velocity
+
+      float t1 = (targetVelocity-velocity)/profileDeceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*period)*period);
+        velocity += profileDeceleration*period;
+        acceleration = profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      }
+
+    } else if (velocity < 0.0f) { // speed up to (negative) target velocity
+
+      float t1 = (velocity-targetVelocity)/profileAcceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*period)*period);
+        velocity += -profileAcceleration*period;
+        acceleration = -profileAcceleration;
+      } else {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t1)*t1);
+        velocity += -profileAcceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      }
+
+    } else { // slow down to zero first, and then speed up to (negative) target velocity
+
+      float t1 = velocity/profileDeceleration;
+      float t2 = -targetVelocity/profileAcceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*period)*period);
+        velocity += -profileDeceleration*period;
+        acceleration = -profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*(period-t1))*(period-t1));
+        velocity += -profileAcceleration*(period-t1);
+        acceleration = -profileAcceleration;
+      } else {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t2)*t2);
+        velocity += -profileAcceleration*t2;
+        position += static_cast<double>(velocity*(period-t1-t2));
+        acceleration = 0.0f;
+      }
+    }
+  }
+}
+
+/**
+ * Increments the current motion towards a given target position.
+ * @param targetPosition the desired target position given in [m] or [rad].
+ * @param period the time period to increment the motion values for, given in [s].
+ */
+void Motion::incrementToPosition(double targetPosition, float period) {
+
+  // calculate position, when velocity is reduced to zero
+
+  double stopPosition = (velocity > 0.0f) ? position+static_cast<double>(velocity*velocity/profileDeceleration*0.5f) : position-static_cast<double>(velocity*velocity/profileDeceleration*0.5f);
+
+  if (targetPosition > stopPosition) { // positive velocity required
+
+    if (velocity > profileVelocity) { // slow down to profile velocity first
+
+      float t1 = (velocity-profileVelocity)/profileDeceleration;
+      float t2 = static_cast<float>(targetPosition-stopPosition)/profileVelocity;
+      float t3 = profileVelocity/profileDeceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*period)*period);
+        velocity += -profileDeceleration*period;
+        acceleration = -profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*(period-t1-t2))*(period-t1-t2));
+        velocity += -profileDeceleration*(period-t1-t2);
+        acceleration = -profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t3)*t3);
+        velocity += -profileDeceleration*t3;
+        acceleration = 0.0f;
+      }
+
+    } else if (velocity > 0.0f) { // speed up to profile velocity
+
+      float t1 = (profileVelocity-velocity)/profileAcceleration;
+      float t3 = profileVelocity/profileDeceleration;
+      float t2 = (static_cast<float>(targetPosition-position)-(velocity+profileVelocity)*0.5f*t1)/profileVelocity-0.5f*t3;
+
+      /*if (t2 < 0.0f) {
+                float maxVelocity = std::sqrt((2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+                t1 = (maxVelocity-velocity)/profileAcceleration;
+                t2 = 0.0f;
+                t3 = maxVelocity/profileDeceleration;
+            }
+            */
+      if (t2 < 0.0f) {
+        float temp((2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+        if (temp < 0.0f) {
+          t1 = 0.0f;
+          t2 = 0.0f;
+          t3 = 0.0f;
+        } else {
+          float maxVelocity(std::sqrt(temp));
+          t1 = (maxVelocity-velocity)/profileAcceleration;
+          t2 = 0.0f;
+          t3 = maxVelocity/profileDeceleration;
+        }
+
+      }
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*period)*period);
+        velocity += profileAcceleration*period;
+        acceleration = profileAcceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t1)*t1);
+        velocity += profileAcceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t1)*t1);
+        velocity += profileAcceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*(period-t1-t2))*(period-t1-t2));
+        velocity += -profileDeceleration*(period-t1-t2);
+        acceleration = -profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t1)*t1);
+        velocity += profileAcceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t3)*t3);
+        velocity += -profileDeceleration*t3;
+        acceleration = 0.0f;
+      }
+
+    } else { // slow down to zero first, and then speed up to profile velocity
+
+      float t1 = -velocity/profileDeceleration;
+      float t2 = profileVelocity/profileAcceleration;
+      float t4 = profileVelocity/profileDeceleration;
+      float t3 = (static_cast<float>(targetPosition-position)-velocity*0.5f*t1)/profileVelocity-0.5f*(t2+t4);
+
+      /*if (t3 < 0.0f) {
+                float maxVelocity = std::sqrt((2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+                t2 = maxVelocity/profileAcceleration;
+                t3 = 0.0f;
+                t4 = maxVelocity/profileDeceleration;
+            }*/
+
+      if ( t3 < 0.0f ) {
+        float temp((2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+
+        if (temp<0.0f) {
+          t2 = 0.0f;
+          t3 = 0.0f;
+          t4 = 0.0f;
+        } else {
+          float maxVelocity( std::sqrt( temp ) );
+          t2 = ( maxVelocity - velocity ) / profileAcceleration;
+          t3 = 0.0f;
+          t4 = maxVelocity / profileDeceleration;
+        }
+      }
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*period)*period);
+        velocity += profileDeceleration*period;
+        acceleration = profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*(period-t1))*(period-t1));
+        velocity += profileAcceleration*(period-t1);
+        acceleration = profileAcceleration;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t2)*t2);
+        velocity += profileAcceleration*t2;
+        position += static_cast<double>(velocity*(period-t1-t2));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3+t4 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t2)*t2);
+        velocity += profileAcceleration*t2;
+        position += static_cast<double>(velocity*t3);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*(period-t1-t2-t3))*(period-t1-t2-t3));
+        velocity += -profileDeceleration*(period-t1-t2-t3);
+        acceleration = -profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>((velocity+profileAcceleration*0.5f*t2)*t2);
+        velocity += profileAcceleration*t2;
+        position += static_cast<double>(velocity*t3);
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t4)*t4);
+        velocity += -profileDeceleration*t4;
+        acceleration = 0.0f;
+      }
+    }
+
+  } else { // negative velocity required
+
+    if (velocity < -profileVelocity) { // slow down to (negative) profile velocity first
+
+      float t1 = (-profileVelocity-velocity)/profileDeceleration;
+      float t2 = static_cast<float>(stopPosition-targetPosition)/profileVelocity;
+      float t3 = profileVelocity/profileDeceleration;
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*period)*period);
+        velocity += profileDeceleration*period;
+        acceleration = profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*(period-t1-t2))*(period-t1-t2));
+        velocity += profileDeceleration*(period-t1-t2);
+        acceleration = profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t1)*t1);
+        velocity += profileDeceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t3)*t3);
+        velocity += profileDeceleration*t3;
+        acceleration = 0.0f;
+      }
+
+    } else if (velocity < 0.0f) { // speed up to (negative) profile velocity
+
+      float t1 = (velocity+profileVelocity)/profileAcceleration;
+      float t3 = profileVelocity/profileDeceleration;
+      float t2 = (static_cast<float>(position-targetPosition)+(velocity-profileVelocity)*0.5f*t1)/profileVelocity-0.5f*t3;
+
+      /*if (t2 < 0.0f) {
+                float minVelocity = -std::sqrt((-2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+                t1 = (velocity-minVelocity)/profileAcceleration;
+                t2 = 0.0f;
+                t3 = -minVelocity/profileDeceleration;
+            }*/
+
+      if (t2 < 0.0f) {
+        float temp((-2.0f*static_cast<float>(targetPosition-position)*profileAcceleration+velocity*velocity)*profileDeceleration/(profileAcceleration+profileDeceleration));
+        if (temp<0.0f) {
+          t1 = 0.0f;
+          t2 = 0.0f;
+          t3 = 0.0f;
+        } else {
+          float minVelocity( -std::sqrt(temp));
+          t1 = (velocity-minVelocity)/profileAcceleration;
+          t2 = 0.0f;
+          t3 = -minVelocity/profileDeceleration;
+        }
+      }
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*period)*period);
+        velocity += -profileAcceleration*period;
+        acceleration = -profileAcceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t1)*t1);
+        velocity += -profileAcceleration*t1;
+        position += static_cast<double>(velocity*(period-t1));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t1)*t1);
+        velocity += -profileAcceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*(period-t1-t2))*(period-t1-t2));
+        velocity += profileDeceleration*(period-t1-t2);
+        acceleration = profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t1)*t1);
+        velocity += -profileAcceleration*t1;
+        position += static_cast<double>(velocity*t2);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t3)*t3);
+        velocity += profileDeceleration*t3;
+        acceleration = 0.0f;
+      }
+
+    } else { // slow down to zero first, and then speed up to (negative) profile velocity
+
+      float t1 = velocity/profileDeceleration;
+      float t2 = profileVelocity/profileAcceleration;
+      float t4 = profileVelocity/profileDeceleration;
+      float t3 = (-static_cast<float>(targetPosition-position)+velocity*0.5f*t1)/profileVelocity-0.5f*(t2+t4);
+
+      /*if (t3 < 0.0f) {
+                float minVelocity = -std::sqrt((-2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+                t2 = -minVelocity/profileAcceleration;
+                t3 = 0.0f;
+                t4 = -minVelocity/profileDeceleration;
+            }*/
+
+      if (t3<0.0f){
+        float temp((-2.0f*static_cast<float>(targetPosition-position)*profileDeceleration+velocity*velocity)*profileAcceleration/(profileAcceleration+profileDeceleration));
+        if (temp < 0.0f) {
+          t2 = 0.0f;
+          t3 = 0.0f;
+          t4 = 0.0f;
+        } else {
+          float minVelocity(-std::sqrt(temp));
+          t2 = -minVelocity/profileAcceleration;
+          t3 = 0.0f;
+          t4 = -minVelocity/profileDeceleration;
+        }
+      }
+
+      if (t1 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*period)*period);
+        velocity += -profileDeceleration*period;
+        acceleration = -profileDeceleration;
+      } else if (t1+t2 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*(period-t1))*(period-t1));
+        velocity += -profileAcceleration*(period-t1);
+        acceleration = -profileAcceleration;
+      } else if (t1+t2+t3 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t2)*t2);
+        velocity += -profileAcceleration*t2;
+        position += static_cast<double>(velocity*(period-t1-t2));
+        acceleration = 0.0f;
+      } else if (t1+t2+t3+t4 > period) {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t2)*t2);
+        velocity += -profileAcceleration*t2;
+        position += static_cast<double>(velocity*t3);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*(period-t1-t2-t3))*(period-t1-t2-t3));
+        velocity += profileDeceleration*(period-t1-t2-t3);
+        acceleration = profileDeceleration;
+      } else {
+        position += static_cast<double>((velocity-profileDeceleration*0.5f*t1)*t1);
+        velocity += -profileDeceleration*t1;
+        position += static_cast<double>((velocity-profileAcceleration*0.5f*t2)*t2);
+        velocity += -profileAcceleration*t2;
+        position += static_cast<double>(velocity*t3);
+        position += static_cast<double>((velocity+profileDeceleration*0.5f*t4)*t4);
+        velocity += profileDeceleration*t4;
+        acceleration = 0.0f;
+      }
+    }
+  }
+}
+