| #!/usr/bin/python3 |
| |
| import numpy |
| import sys, os |
| import casadi |
| from numpy.testing import assert_array_equal, assert_array_almost_equal |
| import unittest |
| |
| from frc971.control_loops.swerve import dynamics |
| |
| |
| def state_vector(velocity=numpy.array([[1.0], [0.0]]), |
| dx=0.0, |
| dy=0.0, |
| theta=0.0, |
| omega=0.0, |
| module_omega=0.0, |
| module_angle=0.0, |
| drive_wheel_velocity=None, |
| module_angles=None): |
| """Returns the state vector with the requested state.""" |
| X_initial = numpy.zeros((25, 1)) |
| # All the wheels are spinning at the speed needed to hit the velocity in m/s |
| drive_wheel_velocity = (drive_wheel_velocity |
| or numpy.linalg.norm(velocity)) |
| |
| X_initial[2, 0] = module_omega |
| X_initial[3, 0] = drive_wheel_velocity / (dynamics.WHEEL_RADIUS) |
| |
| X_initial[6, 0] = module_omega |
| X_initial[7, 0] = drive_wheel_velocity / (dynamics.WHEEL_RADIUS) |
| |
| X_initial[10, 0] = module_omega |
| X_initial[11, 0] = drive_wheel_velocity / (dynamics.WHEEL_RADIUS) |
| |
| X_initial[14, 0] = module_omega |
| X_initial[15, 0] = drive_wheel_velocity / (dynamics.WHEEL_RADIUS) |
| |
| X_initial[0, 0] = module_angle |
| X_initial[4, 0] = module_angle |
| X_initial[8, 0] = module_angle |
| X_initial[12, 0] = module_angle |
| |
| if module_angles is not None: |
| assert (len(module_angles) == 4) |
| X_initial[0, 0] = module_angles[0] |
| X_initial[4, 0] = module_angles[1] |
| X_initial[8, 0] = module_angles[2] |
| X_initial[12, 0] = module_angles[3] |
| |
| X_initial[18, 0] = theta |
| |
| X_initial[19, 0] = velocity[0, 0] + dx |
| X_initial[20, 0] = velocity[1, 0] + dy |
| X_initial[21, 0] = omega |
| |
| return X_initial |
| |
| |
| def wrap(fn): |
| evaluated_fn = fn(casadi.SX.sym("X", 25, 1), casadi.SX.sym("U", 8, 1)) |
| return lambda X, U: numpy.array(evaluated_fn(X, U)) |
| |
| |
| def wrap_module(fn, i): |
| evaluated_fn = fn(i, casadi.SX.sym("X", 25, 1), casadi.SX.sym("U", 8, 1)) |
| return lambda X, U: numpy.array(evaluated_fn(X, U)) |
| |
| |
| class TestSwervePhysics(unittest.TestCase): |
| I = numpy.zeros((8, 1)) |
| |
| def setUp(self): |
| self.swerve_physics = wrap(dynamics.swerve_physics) |
| self.contact_patch_velocity = [ |
| wrap_module(dynamics.contact_patch_velocity, i) for i in range(4) |
| ] |
| self.wheel_ground_velocity = [ |
| wrap_module(dynamics.wheel_ground_velocity, i) for i in range(4) |
| ] |
| self.wheel_slip_velocity = [ |
| wrap_module(dynamics.wheel_slip_velocity, i) for i in range(4) |
| ] |
| self.wheel_force = [ |
| wrap_module(dynamics.wheel_force, i) for i in range(4) |
| ] |
| self.module_angular_accel = [ |
| wrap_module(dynamics.module_angular_accel, i) for i in range(4) |
| ] |
| self.F = [wrap_module(dynamics.F, i) for i in range(4)] |
| self.mounting_location = [ |
| wrap_module(dynamics.mounting_location, i) for i in range(4) |
| ] |
| |
| self.slip_angle = [ |
| wrap_module(dynamics.slip_angle, i) for i in range(4) |
| ] |
| self.slip_ratio = [ |
| wrap_module(dynamics.slip_ratio, i) for i in range(4) |
| ] |
| self.Ms = [wrap_module(dynamics.Ms, i) for i in range(4)] |
| |
| def test_contact_patch_velocity(self): |
| """Tests that the contact patch velocity makes sense.""" |
| for i in range(4): |
| contact_patch_velocity = wrap_module( |
| dynamics.contact_patch_velocity, i) |
| wheel_ground_velocity = wrap_module(dynamics.wheel_ground_velocity, |
| i) |
| |
| # No angular velocity should result in just linear motion. |
| for velocity in [ |
| numpy.array([[1.5], [0.0]]), |
| numpy.array([[0.0], [1.0]]), |
| numpy.array([[-1.5], [0.0]]), |
| numpy.array([[0.0], [-1.0]]), |
| numpy.array([[2.0], [-1.7]]), |
| ]: |
| for theta in [0.0, 1.0, -1.0, 100.0]: |
| patch_velocity = contact_patch_velocity( |
| state_vector(velocity=velocity, theta=theta), self.I) |
| |
| assert_array_equal(patch_velocity, velocity) |
| |
| # Now, test that spinning the robot results in module velocities. |
| # We are assuming that each module is on a square robot. |
| module_center_of_mass_angle = i * numpy.pi / 2.0 + numpy.pi / 4.0 |
| for theta in [-module_center_of_mass_angle, 0.0, 1.0, -1.0, 100.0]: |
| for omega in [0.65, -0.1]: |
| # Point each module to the center to make the math easier. |
| patch_velocity = contact_patch_velocity( |
| state_vector(velocity=numpy.array([[0.0], [0.0]]), |
| theta=theta, |
| omega=omega, |
| module_angle=module_center_of_mass_angle), |
| self.I) |
| |
| assert_array_almost_equal( |
| patch_velocity, |
| (dynamics.ROBOT_WIDTH / numpy.sqrt(2.0) - |
| dynamics.CASTER) * omega * numpy.array([[ |
| -numpy.sin(theta + module_center_of_mass_angle) |
| ], [numpy.cos(theta + module_center_of_mass_angle)]])) |
| |
| # Point the wheel along +x, rotate it by theta, then spin it. |
| # Confirm the velocities come out right. |
| patch_velocity = contact_patch_velocity( |
| state_vector( |
| velocity=numpy.array([[0.0], [0.0]]), |
| theta=-module_center_of_mass_angle, |
| module_omega=omega, |
| module_angle=(theta + |
| module_center_of_mass_angle)), |
| self.I) |
| |
| assert_array_almost_equal( |
| patch_velocity, -dynamics.CASTER * omega * |
| numpy.array([[-numpy.sin(theta)], [numpy.cos(theta)]])) |
| |
| # Now, test that the rotation back to wheel coordinates works. |
| # The easiest way to do this is to point the wheel in a direction, |
| # move in that direction, and confirm that there is no lateral velocity. |
| for robot_angle in [0.0, 1.0, -5.0]: |
| for module_angle in [0.0, 1.0, -5.0]: |
| wheel_patch_velocity = numpy.array( |
| wheel_ground_velocity( |
| state_vector(velocity=numpy.array( |
| [[numpy.cos(robot_angle + module_angle)], |
| [numpy.sin(robot_angle + module_angle)]]), |
| theta=robot_angle, |
| module_angle=module_angle), self.I)) |
| |
| assert_array_almost_equal(wheel_patch_velocity, |
| numpy.array([[1], [0]])) |
| |
| def test_slip_angle(self): |
| """Tests that the slip_angle calculation works.""" |
| velocity = numpy.array([[1.5], [0.0]]) |
| |
| for i in range(4): |
| x = casadi.SX.sym("x") |
| y = casadi.SX.sym("y") |
| half_atan2 = casadi.Function('half_atan2', [y, x], |
| [dynamics.half_atan2(y, x)]) |
| |
| for wrap in range(-3, 3): |
| for theta in [0.0, 0.6, -0.4]: |
| module_angle = numpy.pi * wrap + theta |
| |
| self.assertAlmostEqual( |
| theta, |
| half_atan2(numpy.sin(module_angle), |
| numpy.cos(module_angle))) |
| |
| computed_angle = self.slip_angle[i](state_vector( |
| velocity=velocity, |
| module_angle=numpy.pi * wrap + theta), self.I)[0, 0] |
| |
| self.assertAlmostEqual(theta, computed_angle) |
| |
| def test_wheel_torque(self): |
| """Tests that the per module self aligning forces have the right signs.""" |
| X = state_vector(module_angles=[-0.001, -0.001, 0.001, 0.001]) |
| xdot_equal = self.swerve_physics(X, self.I) |
| |
| self.assertGreater(xdot_equal[2, 0], 0.0) |
| self.assertAlmostEqual(xdot_equal[3, 0], 0.0, places=1) |
| self.assertGreater(self.Ms[0](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_equal[6, 0], 0.0) |
| self.assertAlmostEqual(xdot_equal[7, 0], 0.0, places=1) |
| self.assertGreater(self.Ms[1](X, self.I)[0, 0], 0.0) |
| |
| self.assertLess(xdot_equal[10, 0], 0.0) |
| self.assertAlmostEqual(xdot_equal[11, 0], 0.0, places=1) |
| self.assertLess(self.Ms[2](X, self.I)[0, 0], 0.0) |
| |
| self.assertLess(xdot_equal[14, 0], 0.0) |
| self.assertAlmostEqual(xdot_equal[15, 0], 0.0, places=1) |
| self.assertLess(self.Ms[3](X, self.I)[0, 0], 0.0) |
| |
| # Shouldn't be spinning. |
| self.assertAlmostEqual(xdot_equal[21, 0], 0.0, places=2) |
| |
| # Now, make the bot want to go left. |
| # The wheels will be going too fast based on our calcs, so they should be decelerating. |
| X = state_vector(module_angles=[0.01, 0.01, 0.01, 0.01]) |
| xdot_left = self.swerve_physics(X, self.I) |
| |
| self.assertLess(xdot_left[2, 0], -0.1) |
| self.assertLess(xdot_left[3, 0], 0.0) |
| self.assertLess(self.Ms[0](X, self.I)[0, 0], 0.0) |
| |
| self.assertLess(xdot_left[6, 0], -0.1) |
| self.assertLess(xdot_left[7, 0], 0.0) |
| self.assertLess(self.Ms[1](X, self.I)[0, 0], 0.0) |
| |
| self.assertLess(xdot_left[10, 0], -0.1) |
| self.assertLess(xdot_left[11, 0], 0.0) |
| self.assertLess(self.Ms[2](X, self.I)[0, 0], 0.0) |
| |
| self.assertLess(xdot_left[14, 0], -0.1) |
| self.assertLess(xdot_left[15, 0], 0.0) |
| self.assertLess(self.Ms[3](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_left[19, 0], 0.0001) |
| self.assertGreater(xdot_left[20, 0], 0.1) |
| # Shouldn't be spinning. |
| self.assertAlmostEqual(xdot_left[21, 0], 0.0) |
| |
| # And now do it to the right too. |
| X = state_vector(module_angles=[-0.01, -0.01, -0.01, -0.01]) |
| xdot_right = self.swerve_physics(X, self.I) |
| |
| self.assertGreater(xdot_right[2, 0], 0.1) |
| self.assertLess(xdot_right[3, 0], 0.0) |
| self.assertGreater(self.Ms[0](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_right[6, 0], 0.1) |
| self.assertLess(xdot_right[7, 0], 0.0) |
| self.assertGreater(self.Ms[1](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_right[10, 0], 0.1) |
| self.assertLess(xdot_right[11, 0], 0.0) |
| self.assertGreater(self.Ms[2](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_right[14, 0], 0.1) |
| self.assertLess(xdot_right[15, 0], 0.0) |
| self.assertGreater(self.Ms[3](X, self.I)[0, 0], 0.0) |
| |
| self.assertGreater(xdot_right[19, 0], 0.0001) |
| self.assertLess(xdot_right[20, 0], -0.1) |
| # Shouldn't be spinning. |
| self.assertAlmostEqual(xdot_right[21, 0], 0.0) |
| |
| def test_wheel_forces(self): |
| """Tests that the per module forces have the right signs.""" |
| for i in range(4): |
| wheel_force = wrap_module(dynamics.wheel_force, i) |
| |
| X = state_vector() |
| robot_equal = wheel_force(X, self.I) |
| xdot_equal = self.swerve_physics(X, self.I) |
| self.assertEqual(robot_equal[0, 0], 0.0) |
| self.assertEqual(robot_equal[1, 0], 0.0) |
| self.assertEqual(xdot_equal[2 + 4 * i], 0.0) |
| self.assertEqual(xdot_equal[3 + 4 * i], 0.0) |
| |
| # Robot is moving faster than the wheels, it should decelerate. |
| X = state_vector(dx=0.01) |
| robot_faster = wheel_force(X, self.I) |
| xdot_faster = self.swerve_physics(X, self.I) |
| self.assertLess(robot_faster[0, 0], -0.1) |
| self.assertEqual(robot_faster[1, 0], 0.0) |
| self.assertGreater(xdot_faster[3 + 4 * i], 0.0) |
| |
| # Robot is now going slower than the wheels. It should accelerate. |
| X = state_vector(dx=-0.01) |
| robot_slower = wheel_force(X, self.I) |
| xdot_slower = self.swerve_physics(X, self.I) |
| self.assertGreater(robot_slower[0, 0], 0.1) |
| self.assertEqual(robot_slower[1, 0], 0.0) |
| self.assertLess(xdot_slower[3 + 4 * i], 0.0) |
| |
| # Positive lateral velocity -> negative force. |
| robot_left = wheel_force(state_vector(dy=0.01), self.I) |
| self.assertEqual(robot_left[0, 0], 0.0) |
| self.assertLess(robot_left[1, 0], -0.1) |
| |
| # Negative lateral velocity -> positive force. |
| robot_right = wheel_force(state_vector(dy=-0.01), self.I) |
| self.assertEqual(robot_right[0, 0], 0.0) |
| self.assertGreater(robot_right[1, 0], 0.1) |
| |
| |
| if __name__ == '__main__': |
| unittest.main() |