SCurve

java.lang.Object
- stella.util.SCurve

```
public class SCurve
extends Object
```
A class that simulates the movement of most modern motors, the S-curve movement. This movement is characterized by four different pulses in the jerk (time-derivative of the acceleration), positive, negative, negative, and positive that advances the motor in a very smooth fashion. Accelaration, velocity, and displacement follow curves like
. The s-curve has an analytical solution. This class allows querying of current jerk, acceleration, velocity and distance, as soon as the jerk constant, the α and β time fractions and the distance to travel have been set. For overlaying two S-curve movements, consider that the jerk is the prescribed function, thus from the previous S-curve the acceleration, velocity, and displacement are the boundary conditions to the differential equations. For non-zero BC, the time of the movement gets a cubic equation with non-vanishing quadratic and linear terms. Set non-zero BC with a call to setZero(double, double, double).

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`SCurve.Offset` A test class that reads d, j0, alpha, and beta from the command line and then splits the time into 10000 steps, where current values of the jerk, the acceleration, the velocity, and the distance are printed to system.out.

Field Summary

Fields
Modifier and Type	Field and Description
`private static double`	`ACCURACY` For recursive lengthen/shortening of intervals, accuracy to reach.
`private double`	`aend` The acceleration at end time.
`private double`	`aiterate` During iteration this gets to alpha.
`private double`	`alpha` The current value of the jerk time fraction.
`static double`	`ALPHA` A default value for the jerk time fraction, α.
`private double`	`az` The acceleration at starting time.
`private double`	`beta` The current value of the constant speed time fraction.
`static double`	`BETA` A default value for the constant speed time fraction, β.
`private static double`	`BETAMIN` The minimum beta, if everything fails.
`private double`	`biterate` During iteration this gets to beta.
`private double`	`d` The distance to travel.
`private double`	`delta` The relative change of the constant-acceleration period due to vz.
`private double`	`gamma` The relative change of the constant-jerk periods to compensate az.
`private static int`	`ITERATION` For recursive lengthen/shortening of intervals, maximum iterations
`private double`	`j0` The jerk constant, i.e.
`private double`	`titerate` During iteration this gets to travel time.
`private double`	`tm` The time needed for traveling d, calculated.
`private double`	`ts` Starting time for arbitrary offsets.
`private double`	`vend` The velocity at end time.
`private double`	`vz` The velocity at starting time.
`private double`	`xz` The displacement at starting time.

Constructor Summary

Constructors
Constructor and Description
`SCurve()` Constructs a new s-curve object.
`SCurve(double a, double b)` Constructs a new s-curve object specifying the jerk time fraction and the constatn-speed time fraction.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`private double`	`deriveTravelTime(double j, double al, double be)` Calculates the travel time for non-vanishing BC.
`double`	`getAcceleration(double tnow)` Gets the current acceleration in rad/s^2.
`double`	`getAccMax()` Returns the maximum acceleration excerted within the motor.
`double`	`getDistance(double tnow)` Gets the current distance travelled since the start of the movement, in rad.
`double`	`getJerk(double tnow)` Gets the current jerk.
`private int`	`getRegion(double t)` Returns the index of the region where t is located.
`double`	`getTravelTime()` Return the time required for the offset to complete in seconds.
`double`	`getVelMax()` Returns the maximum speed encountered during the movement.
`double`	`getVelocity(double tnow)` Gets the current speed in rad/s.
`private boolean`	`iterateGammaDelta(double tinit, double j, double al, double be)` Tries to get a solution for gamma, delta that satisfy a=0 & v=0 at end of movement.
`void`	`setConstantSpeedTime(double b)` Specifies a new contant-speed time fraction.
`void`	`setDistance(double dist)` Sets the distance to travel in rad.
`void`	`setJerkConstant(double j)` Sets the jerk constant in rad/s^3.
`void`	`setJerkTime(double a)` Specifies a new jerk-time fraction.
`void`	`setZero(double a0, double v0, double x0)` Sets the boundary condition.
`void`	`startMovement(double start)` Starts the s-curve movement.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - ALPHA
```
public static final double ALPHA
```
    A default value for the jerk time fraction, α.
    
    See Also:
    
    Constant Field Values
  - BETA
```
public static final double BETA
```
    A default value for the constant speed time fraction, β.
    
    See Also:
    
    Constant Field Values
  - ACCURACY
```
private static final double ACCURACY
```
    For recursive lengthen/shortening of intervals, accuracy to reach.
    
    See Also:
    
    Constant Field Values
  - BETAMIN
```
private static final double BETAMIN
```
    The minimum beta, if everything fails.
    
    See Also:
    
    Constant Field Values
  - ITERATION
```
private static final int ITERATION
```
    For recursive lengthen/shortening of intervals, maximum iterations
    
    See Also:
    
    Constant Field Values
  - alpha
```
private double alpha
```
    The current value of the jerk time fraction.
  - beta
```
private double beta
```
    The current value of the constant speed time fraction.
  - gamma
```
private double gamma
```
    The relative change of the constant-jerk periods to compensate az.
  - delta
```
private double delta
```
    The relative change of the constant-acceleration period due to vz.
  - j0
```
private double j0
```
    The jerk constant, i.e. the total jerk in the four jerk times.
  - d
```
private double d
```
    The distance to travel.
  - az
```
private double az
```
    The acceleration at starting time.
  - vz
```
private double vz
```
    The velocity at starting time.
  - xz
```
private double xz
```
    The displacement at starting time.
  - aend
```
private double aend
```
    The acceleration at end time.
  - vend
```
private double vend
```
    The velocity at end time.
  - tm
```
private double tm
```
    The time needed for traveling d, calculated.
  - ts
```
private double ts
```
    Starting time for arbitrary offsets.
  - titerate
```
private double titerate
```
    During iteration this gets to travel time.
  - aiterate
```
private double aiterate
```
    During iteration this gets to alpha.
  - biterate
```
private double biterate
```
    During iteration this gets to beta.
- Constructor Detail
  - SCurve
```
public SCurve()
```
    Constructs a new s-curve object.
  - SCurve
```
public SCurve(double a,
              double b)
```
    Constructs a new s-curve object specifying the jerk time fraction and the constatn-speed time fraction.
- Method Detail
  - setJerkTime
```
public void setJerkTime(double a)
```
    Specifies a new jerk-time fraction. Must be positive and smaller than 0.25.
  - setConstantSpeedTime
```
public void setConstantSpeedTime(double b)
```
    Specifies a new contant-speed time fraction. Must be positive and smaller than one.
  - setJerkConstant
```
public void setJerkConstant(double j)
```
    Sets the jerk constant in rad/s^3. This jerk is exerted on the motor on four different times, starting with positive jerk, then negative, negative, and positive jerk again.
  - setDistance
```
public void setDistance(double dist)
```
    Sets the distance to travel in rad.
  - setZero
```
public void setZero(double a0,
                    double v0,
                    double x0)
```
    Sets the boundary condition. This is the acceleration, the velocity and the displacement at start time.
    
    Parameters:
    
    a0 - The acceleration at start time from previous movement.
    
    v0 - The velocity at start time from previous movement.
    
    x0 - The displacement at start time from previous movement.
  - startMovement
```
public void startMovement(double start)
```
    Starts the s-curve movement. This method throws an exception if the jerk constant or the distance-to-travel are not set. Additionally, if the sign of the jerk is not equal to the sign of the distance, an exception is thrown as in this case the required distance will not be reached in a meaningful way.
    After a start to this method, current distance travelled, speed, acceleration and jerk can be queried.
    
    Parameters:
    
    start - The start time in seconds, used as an offset.
  - getJerk
```
public double getJerk(double tnow)
```
    Gets the current jerk.
    
    Parameters:
    
    tnow - Time in second. Start time is subtracted.
  - getAcceleration
```
public double getAcceleration(double tnow)
```
    Gets the current acceleration in rad/s^2.
    
    Parameters:
    
    tnow - Time in second. Start time is subtracted.
  - getVelocity
```
public double getVelocity(double tnow)
```
    Gets the current speed in rad/s.
    
    Parameters:
    
    tnow - Time in second. Start time is subtracted.
  - getDistance
```
public double getDistance(double tnow)
```
    Gets the current distance travelled since the start of the movement, in rad. Note that formulars are for antisymmetric x, thus the half offset is added at each region.
    
    Parameters:
    
    tnow - Time in second. Start time is subtracted.
  - getAccMax
```
public double getAccMax()
```
    Returns the maximum acceleration excerted within the motor. This acceleration is experienced two times, shortly after the start of the movement and again close to the end of the movement.
  - getVelMax
```
public double getVelMax()
```
    Returns the maximum speed encountered during the movement. This speed occurs around the middle of the movement, its length fraction equals β. Note that this maximum velocity has an alpha-independant relation to the average velocity according to
```
       v_max=2./(1+β)ċv_av.
       
```
  - getTravelTime
```
public double getTravelTime()
```
    Return the time required for the offset to complete in seconds.
  - getRegion
```
private int getRegion(double t)
```
    Returns the index of the region where t is located. -1 and 7 denote regions outside the main movement.
  - deriveTravelTime
```
private double deriveTravelTime(double j,
                                double al,
                                double be)
```
    Calculates the travel time for non-vanishing BC. Uses Newton approximation, starting value is the solution of the cubic equation in travel time. Takes primary time fraction as arguments.
  - iterateGammaDelta
```
private boolean iterateGammaDelta(double tinit,
                                  double j,
                                  double al,
                                  double be)
```
    Tries to get a solution for gamma, delta that satisfy a=0 & v=0 at end of movement.

Class SCurve

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ALPHA

BETA

ACCURACY

BETAMIN

ITERATION

alpha

beta

gamma

delta

j0

d

az

vz

xz

aend

vend

tm

ts

titerate

aiterate

biterate

Constructor Detail

SCurve

SCurve

Method Detail

setJerkTime

setConstantSpeedTime

setJerkConstant

setDistance

setZero

startMovement

getJerk

getAcceleration

getVelocity

getDistance

getAccMax

getVelMax

getTravelTime

getRegion

deriveTravelTime

iterateGammaDelta