Quintic Turn

Parameters
No file loaded Load a Param TXT file generated from a previous calculation

Full Constant Radius Calculate based on a varying radius (Full) or Constant Radius throughout the turn

Set r to a commonly used radius. Select Spin Radius to set radius to zero, or Pivot Radius to set radius to half of L
Sym	Values	Unit
Δθ		deg Turn angle (deg). +ve to turn left, -ve to turn right
Δt		s Duration of turn (s). Preferably in multiples of sampling interval
H_f	Final degrees of "faster motor" (deg), can be -ve. If degrees to turn is -ve, this belongs to the left motor. If +ve, then it is the right motor's Expected constant radius. +ve for the turn pivot to be on the left, and -ve for right. Radius may not be constant if the velocities are not assigned properly	deg
L̇_i Left motor's initial velocity, in terms of EV3 medium motor (MM) or EV3 large motor (LM) power. Make sure the magnitude does not exceed the tapering point, which depends on the motor load. In general, the tapering point is 80 for LM, and 70 for MM.	Left motor's initial velocity, in terms of EV3 medium motor (MM) or EV3 large motor (LM) power. Make sure the magnitude does not exceed the tapering point, which depends on the motor load. In general, the tapering point is 80 for LM, and 70 for MM.	MM: 15.6·deg·s^-1 LM: 10.5·deg·s^-1 Unit of 1 LEGO Power. LEGO power is a measurement of speed, pegged to the EV3 medium motor's (MM) or EV3 large motor's (LM) maximum rated angular speed. 1 EV3 MM Power = 15.6 deg/s, 1 EV3 LM Power = 10.6 deg/s.
Ṙ_i	Right motor's initial velocity, in terms of MM or LM power
L̇_f	Left motor's final velocity, in terms MM or LM power
Ṙ_f	Right motor's final velocity, in terms MM or LM power
W		mm Motorised wheels diameter (mm). Assumes both left and right wheels are identical. May be smaller than what you measure.
L		mm Axle track (mm). Separation between centre of both motorised wheels. May not be centre depending on structure of robot or wheel thickness
T		s Sampling Interval (s). Preferably at 0.05s. The EV3 processor can respond well enough if the loop iteration interval is at 0.05s
Invert Left Invert Right Motor inversion, affects only RTF output. If a motor is inverted, whatever velocity values displayed here will be multiplied by -1 in the RTF file. Useful if MM are used for locomotion


RTF Param RTF files and Param TXT file. RTF for velocity output for left and right motors. Odd lines are left, even lines are right. The first line belongs to the left motor. Param contains the RTF file names and all parameters used in the calculation, so you may reload them to view or adjust the parameters at another time

Parameters

No file loaded

Load a Param TXT file generated from a previous calculation

Full Constant Radius

Calculate based on a varying radius (Full) or Constant Radius throughout the turn

Set r to a commonly used radius. Select Spin Radius to set radius to zero, or Pivot Radius to set radius to half of L

Sym

Values

Unit

Δθ

deg

Turn angle (deg). +ve to turn left, -ve to turn right

Δt

Duration of turn (s). Preferably in multiples of sampling interval

H_f

Final degrees of "faster motor" (deg), can be -ve. If degrees to turn is -ve, this belongs to the left motor. If +ve, then it is the right motor's

Expected constant radius. +ve for the turn pivot to be on the left, and -ve for right. Radius may not be constant if the velocities are not assigned properly

deg

L̇_i

Left motor's initial velocity, in terms of EV3 medium motor (MM) or EV3 large motor (LM) power. Make sure the magnitude does not exceed the tapering point, which depends on the motor load. In general, the tapering point is 80 for LM, and 70 for MM.

MM:
15.6·deg·s^-1

LM:
10.5·deg·s^-1

Unit of 1 LEGO Power. LEGO power is a measurement of speed, pegged to the EV3 medium motor's (MM) or EV3 large motor's (LM) maximum rated angular speed. 1 EV3 MM Power = 15.6 deg/s, 1 EV3 LM Power = 10.6 deg/s.

Ṙ_i

Right motor's initial velocity, in terms of MM or LM power

L̇_f

Left motor's final velocity, in terms MM or LM power

Ṙ_f

Right motor's final velocity, in terms MM or LM power

Motorised wheels diameter (mm). Assumes both left and right wheels are identical. May be smaller than what you measure.

Axle track (mm). Separation between centre of both motorised wheels. May not be centre depending on structure of robot or wheel thickness

Sampling Interval (s). Preferably at 0.05s. The EV3 processor can respond well enough if the loop iteration interval is at 0.05s

Invert Left Invert Right

Motor inversion, affects only RTF output. If a motor is inverted, whatever velocity values displayed here will be multiplied by -1 in the RTF file. Useful if MM are used for locomotion

RTF Param

RTF files and Param TXT file. RTF for velocity output for left and right motors. Odd lines are left, even lines are right. The first line belongs to the left motor. Param contains the RTF file names and all parameters used in the calculation, so you may reload them to view or adjust the parameters at another time

Calculated Parameters
Sym	Min	Max	Final	Unit
L	N/A	N/A	N/A	deg Left motor's degrees
R	N/A	N/A	N/A	deg Right motor's degrees
L̇ Left motor's power. Make sure that the magnitude does not exceed 70 (MM) or 80 (LM) or some other power depending on your motor load	N/A	N/A	N/A	N/A
Ṙ Right motor's power. Make sure that the magnitude does not exceed 70 (MM) or 80 (LM) or some other power depending on your motor load	N/A	N/A	N/A	N/A
L̈ Left motor's acceleration (power·s^-1). This is proportional to force, and hence a high magnitude can result in skidding	N/A	N/A	N/A	N/A
R̈ Right motor's acceleration (power·s^-1). This is proportional to force, and hence a high magnitude can result in skidding	N/A	N/A	N/A	N/A
L̊ Left motor's acceleration derivative (power·s^-2). This is proportional to jerk, the derivative of force, and hence a high magnitude can result in skidding	N/A	N/A	N/A	N/A
R̊ Right motor's acceleration derivative (power·s^-2). This is proportional to jerk, the derivative of force, and hence a high magnitude can result in skidding	N/A	N/A	N/A	N/A
x	N/A	N/A	N/A	mm Displacement in the initial forward direction (mm)
y	N/A	N/A	N/A	mm Displacement in the initial left direction (mm)
θ	N/A	N/A	N/A	deg Turn angle (deg)
r	N/A	N/A	N/A	mm Turn radius (mm)

Calculated Parameters

Sym

Min

Max

Final

Unit

N/A

deg

Left motor's degrees

N/A

deg

Right motor's degrees

L̇

Left motor's power. Make sure that the magnitude does not exceed 70 (MM) or 80 (LM) or some other power depending on your motor load

N/A

Ṙ

Right motor's power. Make sure that the magnitude does not exceed 70 (MM) or 80 (LM) or some other power depending on your motor load

N/A

L̈

Left motor's acceleration (power·s^-1). This is proportional to force, and hence a high magnitude can result in skidding

N/A

R̈

Right motor's acceleration (power·s^-1). This is proportional to force, and hence a high magnitude can result in skidding

N/A

L̊

Left motor's acceleration derivative (power·s^-2). This is proportional to jerk, the derivative of force, and hence a high magnitude can result in skidding

N/A

R̊

Right motor's acceleration derivative (power·s^-2). This is proportional to jerk, the derivative of force, and hence a high magnitude can result in skidding

N/A

Displacement in the initial forward direction (mm)

N/A

Displacement in the initial left direction (mm)

N/A

deg

Turn angle (deg)

N/A

Turn radius (mm)

Trajectory

Robot Orientation

Motor Angle

Motor Angular Velocity

Motor Angular Acceleration

Turn Radius

Numeric Equation (Left)
Sym	Values	Unit
L		0	t	deg
+	0	t³
+	0	t⁴
+	0	t⁵
L̇		0		N/A
+	0	t²
+	0	t³
+	0	t⁴
L̈		0	t	N/A
+	0	t²
+	0	t³

Numeric Equation (Left)

Sym

Values

Unit

deg

t³

t⁴

t⁵

L̇

N/A

t²

t³

t⁴

L̈

N/A

t²

t³

Numeric Equation (Right)
Sym	Values	Unit
R		0	t	deg
+	0	t³
+	0	t⁴
+	0	t⁵
Ṙ		0		N/A
+	0	t²
+	0	t³
+	0	t⁴
R̈		0	t	N/A
+	0	t²
+	0	t³

Numeric Equation (Right)

Sym

Values

Unit

deg

t³

t⁴

t⁵

Ṙ

N/A

t²

t³

t⁴

R̈

N/A

t²

t³