Designed a velocity controller for the series elastic intake.
It's stable! This gives us a place to start for controlling it.
We'll have to try it in real life at some point to see if it's right.
Change-Id: I09381b7cba42084f9d5052f54197616fd9dd8c2c
diff --git a/y2018/control_loops/python/intake_simple.py b/y2018/control_loops/python/intake_simple.py
new file mode 100644
index 0000000..9b6ffb1
--- /dev/null
+++ b/y2018/control_loops/python/intake_simple.py
@@ -0,0 +1,273 @@
+#!/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
+
+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
+
+ 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):
+ 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))
+ theta, 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
+
+ return 2.0 * time
+
+def main():
+ # m/sec^2 Gravity Constant
+ gravity = 9.8
+ # m/sec^2 Gravity Constant - Use 0.0 for the intake. It is horizontal.
+ gravity = 0.0
+ # Volts
+ voltage_nominal = 12
+
+ # 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
+ # m Length of arm connected to the robot base
+ length_proximal_arm = inches_to_meters * 47.34
+ # m Length of arm that holds the cube
+ length_distal_arm = inches_to_meters * 44.0
+ # m Length of intake arm from the pivot point to where the big roller contacts a cube.
+ length_intake_arm = inches_to_meters * 9.0
+ 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
+ # m Length from arm pivot point to arm CG
+ 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
+
+ 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
+ # Kg m^2 Moment of inertia of the distal arm
+ J_distal_arm = radius_to_distal_arm_cg * radius_to_distal_arm_cg * mass_distal_arm
+ # Moment of inertia of the arm with the cube on the end
+ J = J_distal_arm_and_cube_at_end_of_proximal_arm + J_proximal_arm
+ # 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()