stella.util
Class 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

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

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

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

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.