Python scripts for selecting 2018 gear ratios for arms and intake.
Change-Id: I8584bc37c3c349997b632b149781ca0329f4244b
diff --git a/y2018/control_loops/python/intake.py b/y2018/control_loops/python/intake.py
new file mode 100755
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+++ b/y2018/control_loops/python/intake.py
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+#!/usr/bin/python3
+
+# This code was used to select the gear ratio for the intake.
+# Run it from the command line and it displays the time required
+# to rotate the intake 180 degrees.
+#
+# Michael Schuh
+# January 20, 2018
+
+import math
+import numpy
+import scipy.integrate
+
+# apt-get install python-scipy python3-scipy python-numpy python3-numpy
+
+pi = math.pi
+pi2 = 2.0*pi
+rad_to_deg = 180.0/pi
+inches_to_meters = 0.0254
+lbs_to_kg = 1.0/2.2
+newton_to_lbf = 0.224809
+newton_meters_to_ft_lbs = 0.73756
+run_count = 0
+theta_travel = 0.0
+
+def to_deg(angle):
+ return (angle*rad_to_deg)
+
+def to_rad(angle):
+ return (angle/rad_to_deg)
+
+def to_rotations(angle):
+ return (angle/pi2)
+
+def time_derivative(x, t, voltage, c1, c2, c3):
+ global run_count
+ theta, omega = x
+ dxdt = [omega, -c1*omega + c3*math.sin(theta) + c2*voltage]
+ run_count = run_count + 1
+
+ #print ('dxdt = ',dxdt,' repr(dxdt) = ', repr(dxdt))
+ return dxdt
+
+def get_distal_angle(theta_proximal):
+ # For the proximal angle = -50 degrees, the distal angle is -180 degrees
+ # For the proximal angle = 10 degrees, the distal angle is -90 degrees
+ distal_angle = to_rad(-180.0 - (-50.0-to_deg(theta_proximal))*(180.0-90.0)/(50.0+10.0))
+ return distal_angle
+
+
+def get_180_degree_time(c1,c2,c3,voltage,gear_ratio,motor_free_speed):
+ #print ("# step time theta angular_speed angular_acceleration theta angular_speed motor_speed motor_speed_fraction")
+ #print ("# (sec) (rad) (rad/sec) (rad/sec^2) (rotations) (rotations/sec) (rpm) (fraction)")
+ global run_count
+ global theta_travel
+
+ if ( True ):
+ # Gravity is assisting the motion.
+ theta_start = 0.0
+ theta_target = pi
+ elif ( False ):
+ # Gravity is assisting the motion.
+ theta_start = 0.0
+ theta_target = -pi
+ elif ( False ):
+ # Gravity is slowing the motion.
+ theta_start = pi
+ theta_target = 0.0
+ elif ( False ):
+ # Gravity is slowing the motion.
+ theta_start = -pi
+ theta_target = 0.0
+ elif ( False ):
+ # This is for the proximal arm motion.
+ theta_start = to_rad(-50.0)
+ theta_target = to_rad(10.0)
+
+ theta_half = 0.5*(theta_start + theta_target)
+ if (theta_start > theta_target):
+ voltage = -voltage
+ theta = theta_start
+ theta_travel = theta_start - theta_target
+ if ( run_count == 0 ):
+ print ("# Theta Start = %.2f radians End = %.2f Theta travel %.2f Theta half = %.2f Voltage = %.2f" % (theta_start,theta_target,theta_travel,theta_half, voltage))
+ print ("# Theta Start = %.2f degrees End = %.2f Theta travel %.2f Theta half = %.2f Voltage = %.2f" % (to_deg(theta_start),to_deg(theta_target),to_deg(theta_travel),to_deg(theta_half), voltage))
+ omega = 0.0
+ time = 0.0
+ delta_time = 0.01 # time step in seconds
+ for step in range(1, 5000):
+ t = numpy.array([time, time + delta_time])
+ time = time + delta_time
+ x = [theta, omega]
+ angular_acceleration = -c1*omega + c2*voltage
+ x_n_plus_1 = scipy.integrate.odeint(time_derivative,x,t,args=(voltage,c1,c2,c3))
+ #print ('x_n_plus_1 = ',x_n_plus_1)
+ #print ('repr(x_n_plus_1) = ',repr(x_n_plus_1))
+ theta, omega = x_n_plus_1[1]
+ #theta= x_n_plus_1[0]
+ #omega = x_n_plus_1[1]
+ if ( False ):
+ print ("%4d %8.4f %8.2f %8.4f %8.4f %8.3f %8.3f %8.3f %8.3f" % \
+ (step, time, theta, omega, angular_acceleration, to_rotations(theta), \
+ to_rotations(omega), omega*gear_ratio*60.0/pi2, omega*gear_ratio/motor_free_speed ))
+ if (theta_start < theta_target):
+ # Angle is increasing through the motion.
+ if (theta > theta_half):
+ break
+ else:
+ # Angle is decreasing through the motion.
+ if (theta < theta_half):
+ break
+
+ #print ("# step time theta angular_speed angular_acceleration theta angular_speed motor_speed motor_speed_fraction")
+ #print ("# (sec) (rad) (rad/sec) (rad/sec^2) (rotations) (rotations/sec) (rpm) (fraction)")
+ #print ("# Total time for 1/2 rotation of arm is %0.2f" % (time*2))
+ return (2.0*time)
+
+def main():
+ gravity = 9.8 # m/sec^2 Gravity Constant
+ gravity = 0.0 # m/sec^2 Gravity Constant - Use 0.0 for the intake. It is horizontal.
+ voltage_nominal = 12 # Volts
+
+ # Vex 775 Pro motor specs from http://banebots.com/p/M2-RS550-120
+ motor_name = "Vex 775 Pro motor specs from http://banebots.com/p/M2-RS550-120"
+ current_stall = 134 # amps stall current
+ current_no_load = 0.7 # amps no load current
+ torque_stall = 710/1000.0 # N-m Stall Torque
+ speed_no_load_rpm = 18730 # RPM no load speed
+
+ if ( True ):
+ # Bag motor from https://www.vexrobotics.com/217-3351.html
+ motor_name = "Bag motor from https://www.vexrobotics.com/217-3351.html"
+ current_stall = 53.0 # amps stall current
+ current_no_load = 1.8 # amps no load current
+ torque_stall = 0.4 # N-m Stall Torque
+ speed_no_load_rpm = 13180.0 # RPM no load speed
+
+ if ( False ):
+ # Mini CIM motor from https://www.vexrobotics.com/217-3371.html
+ motor_name = "Mini CIM motor from https://www.vexrobotics.com/217-3371.html"
+ current_stall = 89.0 # amps stall current
+ current_no_load = 3.0 # amps no load current
+ torque_stall = 1.4 # N-m Stall Torque
+ speed_no_load_rpm = 5840.0 # RPM no load speed
+
+ # How many motors are we using?
+ num_motors = 1
+
+ # Motor values
+ print ("# Motor: %s" % (motor_name))
+ print ("# Number of motors: %d" % (num_motors))
+ print ("# Stall torque: %.1f n-m" % (torque_stall))
+ print ("# Stall current: %.1f amps" % (current_stall))
+ print ("# No load current: %.1f amps" % (current_no_load))
+ print ("# No load speed: %.0f rpm" % (speed_no_load_rpm))
+
+ # Constants from motor values
+ resistance_motor = voltage_nominal/current_stall
+ speed_no_load_rps = speed_no_load_rpm/60.0 # Revolutions per second no load speed
+ speed_no_load = speed_no_load_rps*2.0*pi
+ Kt = num_motors*torque_stall/current_stall # N-m/A torque constant
+ Kv_rpm = speed_no_load_rpm /(voltage_nominal - resistance_motor*current_no_load) # rpm/V
+ Kv = Kv_rpm*2.0*pi/60.0 # rpm/V
+
+ # Robot Geometry and physics
+ length_proximal_arm = inches_to_meters*47.34 # m Length of arm connected to the robot base
+ length_distal_arm = inches_to_meters*44.0 # m Length of arm that holds the cube
+ length_intake_arm = inches_to_meters*9.0 # m Length of intake arm from the pivot point to where the big roller contacts a cube.
+ mass_cube = 6.0*lbs_to_kg # Weight of the cube in Kgrams
+ mass_proximal_arm = 5.5*lbs_to_kg # Weight of proximal arm
+ mass_distal_arm = 3.5*lbs_to_kg # Weight of distal arm
+ mass_distal = mass_cube + mass_distal_arm
+ mass_proximal = mass_proximal_arm + mass_distal
+ radius_to_proximal_arm_cg = 22.0*inches_to_meters # m Length from arm pivot point to arm CG
+ radius_to_distal_arm_cg = 10.0*inches_to_meters # m Length from arm pivot point to arm CG
+
+ radius_to_distal_cg = ( length_distal_arm*mass_cube + radius_to_distal_arm_cg*mass_distal_arm)/mass_distal
+ radius_to_proximal_cg = ( length_proximal_arm*mass_distal + radius_to_proximal_arm_cg*mass_proximal_arm)/mass_proximal
+ J_cube = length_distal_arm*length_distal_arm*mass_cube
+ # Kg m^2 Moment of inertia of the proximal arm
+ J_proximal_arm = radius_to_proximal_arm_cg*radius_to_proximal_arm_cg*mass_distal_arm
+ # Kg m^2 Moment of inertia distal arm and cube at end of proximal arm.
+ J_distal_arm_and_cube_at_end_of_proximal_arm = length_proximal_arm*length_proximal_arm*mass_distal
+ J_distal_arm = radius_to_distal_arm_cg*radius_to_distal_arm_cg*mass_distal_arm # Kg m^2 Moment of inertia of the distal arm
+ J = J_distal_arm_and_cube_at_end_of_proximal_arm + J_proximal_arm # Moment of inertia of the arm with the cube on the end
+ # Intake claw
+ J_intake = 0.295 # Kg m^2 Moment of inertia of intake
+ J = J_intake
+
+ gear_ratio = 140.0 # Guess at the gear ratio
+ gear_ratio = 100.0 # Guess at the gear ratio
+ gear_ratio = 90.0 # Guess at the gear ratio
+
+ error_margine = 1.0
+ voltage = 10.0 # voltage for the motor. Assuming a loaded robot so not using 12 V.
+ # It might make sense to use a lower motor frees peed when the voltage is not a full 12 Volts.
+ # motor_free_speed = Kv*voltage
+ motor_free_speed = speed_no_load
+
+ print ("# Kt = %f N-m/A\n# Kv_rpm = %f rpm/V\n# Kv = %f radians/V" % (Kt, Kv_rpm, Kv))
+ print ("# %.2f Ohms Resistance of the motor " % (resistance_motor))
+ print ("# %.2f kg Cube weight" % (mass_cube))
+ print ("# %.2f kg Proximal Arm mass" % (mass_proximal_arm))
+ print ("# %.2f kg Distal Arm mass" % (mass_distal_arm))
+ print ("# %.2f kg Distal Arm and Cube weight" % (mass_distal))
+ print ("# %.2f m Length from distal arm pivot point to arm CG" % (radius_to_distal_arm_cg))
+ print ("# %.2f m Length from distal arm pivot point to arm and cube cg" % (radius_to_distal_cg))
+ print ("# %.2f kg-m^2 Moment of inertia of the cube about the arm pivot point" % (J_cube))
+ print ("# %.2f m Length from proximal arm pivot point to arm CG" % (radius_to_proximal_arm_cg))
+ print ("# %.2f m Length from proximal arm pivot point to arm and cube cg" % (radius_to_proximal_cg))
+ print ("# %.2f m Proximal arm length" % (length_proximal_arm))
+ print ("# %.2f m Distal arm length" % (length_distal_arm))
+
+ print ("# %.2f kg-m^2 Moment of inertia of the intake about the intake pivot point" % (J_intake))
+ print ("# %.2f kg-m^2 Moment of inertia of the distal arm about the arm pivot point" % (J_distal_arm))
+ print ("# %.2f kg-m^2 Moment of inertia of the proximal arm about the arm pivot point" % (J_proximal_arm))
+ print ("# %.2f kg-m^2 Moment of inertia of the distal arm and cube mass about the proximal arm pivot point" % (J_distal_arm_and_cube_at_end_of_proximal_arm))
+ print ("# %.2f kg-m^2 Moment of inertia of the intake the intake pivot point (J value used in simulation)" % (J))
+ print ("# %d Number of motors" % (num_motors))
+
+ print ("# %.2f V Motor voltage" % (voltage))
+ for gear_ratio in range(60, 241, 10):
+ c1 = Kt*gear_ratio*gear_ratio/(Kv*resistance_motor*J)
+ c2 = gear_ratio*Kt/(J*resistance_motor)
+ c3 = radius_to_proximal_cg*mass_proximal*gravity/J
+
+ if ( False ):
+ print ("# %.8f 1/sec C1 constant" % (c1))
+ print ("# %.2f 1/sec C2 constant" % (c2))
+ print ("# %.2f 1/(V sec^2) C3 constant" % (c3))
+ print ("# %.2f RPM Free speed at motor voltage" % (voltage*Kv_rpm))
+
+ torque_90_degrees = radius_to_distal_cg*mass_distal*gravity
+ voltage_90_degrees = resistance_motor*torque_90_degrees/(gear_ratio*Kt)
+ torque_peak = gear_ratio*num_motors*torque_stall
+ torque_peak_ft_lbs = torque_peak * newton_meters_to_ft_lbs
+ normal_force = torque_peak/length_intake_arm
+ normal_force_lbf = newton_to_lbf*normal_force
+ time_required = get_180_degree_time(c1,c2,c3,voltage,gear_ratio,motor_free_speed)
+ print ("Time for %.1f degrees for gear ratio %3.0f is %.2f seconds. Peak (stall) torque %3.0f nm %3.0f ft-lb Normal force at intake end %3.0f N %2.0f lbf" % \
+ (to_deg(theta_travel),gear_ratio,time_required,
+ torque_peak,torque_peak_ft_lbs,normal_force,normal_force_lbf))
+
+if __name__ == '__main__':
+ main()