Raw values to percentage (light sensor):

percentage = 146 - raw value / 7

Raw values to temperatures, in C° (temperature sensor):

C° = (785 - raw value) / 8

Conversion of Celsius to Fahrenheit degrees:

F° = C° x 9 / 5 + 32

Simple average:

A = (V, +V₂+... +V_n)/n

Weighted average:

A = (V₁xW,+V₂xW₂ + .,. + V_nxW_n) / (W, + W₂ + ... + W_n)

Exponential smoothing:

A_n = (V_n xW, + A_n-1 x W₂) / (W, + W₂)

Linear interpolation: Find the value of the dependent variable Y for a given value of the independent variable X, knowing that for X equal to X_a, Y isY_a, and for X equal to X_b, Y is Y_b.

(Y - Y_a) / (Y_b - Y_a) = (X - X_a) / (X_b - X_a)

Y = (X - X_a) x (Y_b - Y_a) / (Xb - X_a) + Y_a

Equation of the straight line which connects the points (X_a, Y_a) and (X_b, Y_b):

m = (Y_b - Y_a) / (X_b - X_a)

b = Y_a - m x X _a

Y=mxX+b

Output angular velocity of the body of a differential gear Oav, given the input angular velocity of the two axles Iav₁ and Iav₂:

Oav = (lav, + lav₂) / 2

Distance, Time, Speed:

distance = speed x time

speed = distance / time

Circumference C of a wheel, given the diameter D:

C = D x□

□ = 3.1415926...

Increment in rotation sensor count I that corresponds to a turn of the wheel, given R the resolution of the sensor and G the gear ratio between the wheel and the sensor:

l = GxR

R = 16 (for Lego rotation sensors)

Conversion factor F which measures the traveled distance of a wheel for any single increment in the count of a rotation sensor:

F = C / I = (D x □) / (G x R)

Actual traveled distance, given F and the count of the sensor:

T = Count x F

Traveled distance T_c of a differential drive robot’s centerpoint, given the traveled distances T_L andT_R of its left and right drive wheels:

T_c = (T_{R +} T_L)/2

Change of orientation □O_R, in radians, of a differential drive robot, given the traveled distances T_L andT_R of its left and right drive wheels, and the distance B between the wheels:

□O_R = (T_R-T_L)/B

New orientation 0_i of a robot after a change in orientation □O from the previous orientation O_i-1:

O_i = O_i-1 + □O

New position of a robot (x_i, y_i) of a robot after having covered a distance T_c in direction 0_i from position (x_i-1y_i-1):

x_i = x_i-1 + T_c x cos O_i

y_i = y_i-1 + T^c x sin O_i

Conversion of radians to degrees:

Degrees = Radians x 180 / □

Required increment in rotation sensor count for a given change of orientation □O_R in radians or □O_D in degrees:

Count = T / F = (□O_R x B / 2) / F = □O_R x B / 2F

Count = □O_D x π x B / (360 x F)