From ad7ed8157dedbacb4fb30841bd3b7f08d5a5232b Mon Sep 17 00:00:00 2001 From: radu_dell Date: Tue, 22 Sep 2026 18:28:32 +0200 Subject: [PATCH 01/14] Adds downwash implementation from the ETH paper with constant power assumption --- examples/plugins/downwash.py | 139 +++++++++++++++++++++++++++++++++++ 1 file changed, 139 insertions(+) create mode 100644 examples/plugins/downwash.py diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py new file mode 100644 index 00000000..1f2e34e5 --- /dev/null +++ b/examples/plugins/downwash.py @@ -0,0 +1,139 @@ +"""Minimal far-field downwash thrust-loss plugin. + +This models the downwash of level, hovering, identical Crazyflies using the +far-field jet from Bauersfeld et al. (arXiv:2403.13321). It belongs after +``force_torque_controller`` and before ``clip_rotor_vel_cmd``. +""" + +from __future__ import annotations + +from typing import TYPE_CHECKING + +import jax +import jax.numpy as jnp +import numpy as np + +from crazyflow.control.mellinger import force_torque2rotor_vel +from crazyflow.sim.pipeline import insert_fn_before + +if TYPE_CHECKING: + from crazyflow.sim import Sim + from crazyflow.sim.data import SimData + +# Physical parameters for the cf21B_500 +AIR_DENSITY = 1.225 # kg/m^3 +PROPELLER_RADIUS = 27.5e-3 # m +MOTOR_DISTANCE = 0.035355*2 # m, distance between opposite motors +N_PROPELLERS = 4 +GRAVITY = 9.81 + +# Far-field fit in Eq. (9) of the paper. +BD = 10.11 +S = 0.07668 +S0 = -5.817 + + +def _thrust_loss(alpha: jax.Array) -> jax.Array: + """Return T_effective / T_nominal at constant aerodynamic power. + + Equating the still-air and downwash momentum-theory powers yields the + positive root of eta**3 + alpha * eta - 1 = 0, with alpha = U_D / U_H. + """ + lower = jnp.zeros_like(alpha) + upper = jnp.ones_like(alpha) + + def bisect(_: int, bounds: tuple[jax.Array, jax.Array]) -> tuple[jax.Array, jax.Array]: + lower, upper = bounds + eta = (lower + upper) / 2.0 + above_root = eta**3 + alpha * eta > 1.0 + return jnp.where(above_root, lower, eta), jnp.where(above_root, eta, upper) + + lower, upper = jax.lax.fori_loop(0, 24, bisect, (lower, upper)) + return (lower + upper) / 2.0 + + +def downwash_fn(data: SimData) -> SimData: + """Reduce every lower drone's nominal rotor force by its downwash loss.""" + # Axis 1 indexes the source drone; axis 2 indexes the target drone. + source_to_target = data.states.pos[:, :, None, :] - data.states.pos[:, None, :, :] + s = source_to_target[..., 2] # Positive only for targets below a source. + r = jnp.linalg.vector_norm(source_to_target[..., :2], axis=-1) + s_normalized = s / MOTOR_DISTANCE + + mass = data.params.mass[0] + u_hover = jnp.sqrt( + mass * GRAVITY + / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) + ) + half_width = S * (s_normalized - S0) + centerline_velocity = u_hover * BD / (s_normalized - S0) + xi = (r / MOTOR_DISTANCE) / half_width + u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 + u_downwash = jnp.where(s_normalized > 2.5, u_downwash, 0.0) + u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target. + + eta = _thrust_loss(u_downwash / u_hover) + force_torque = data.controls.force_torque + + # Scale only thrust + effective_thrust = force_torque.cmd[..., 0] * eta + + rotor_vel = force_torque2rotor_vel( + effective_thrust[..., None], force_torque.cmd[..., 1:], **force_torque.params + ) + return data.replace(controls=data.controls.replace(rotor_vel=rotor_vel)) + + +def install_downwash(sim: Sim) -> None: + """Add downwash after allocation and rebuild the compiled step function.""" + insert_fn_before(sim.step_pipeline, "clip_rotor_vel_cmd", downwash_fn) + sim.build_step_fn() + + +def main(plot: bool = True) -> None: + """Hover drone 0 while drone 1 flies straight through its downwash.""" + from crazyflow.sim import Sim + + sim = Sim(n_drones=2, drone="cf21B_500", control="state") + install_downwash(sim) + + upper_pos = np.array([0.0, 0.0, 1.2]) + lower_start = np.array([-0.5, 0.0, 1.0]) + sim.data = sim.data.replace( + states=sim.data.states.replace(pos=jnp.array([[upper_pos, lower_start]])) + ) + sim.build_default_data() + + duration = 3.0 + speed = 1.0 / duration + command = np.zeros((1, 2, 16)) + command[..., 9:13] = [0.0, 0.0, 0.0, 1.0] # level quaternion (xyzw) + command[0, 0, :3] = upper_pos + z_positions = [] + + for step in range(int(duration * sim.control_freq)): + t = step / sim.control_freq + command[0, 1, :3] = [-0.5 + speed * t, 0.0, 1.0] + command[0, 1, 3:6] = [speed, 0.0, 0.0] + sim.state_control(command) + sim.step(sim.freq // sim.control_freq) + z_positions.append(np.asarray(sim.data.states.pos[0, :, 2])) + sim.render() + + sim.close() + if plot: + import matplotlib.pyplot as plt + + t = np.arange(len(z_positions)) / sim.control_freq + z_positions = np.asarray(z_positions) + plt.plot(t, z_positions[:, 0], label="upper drone") + plt.plot(t, z_positions[:, 1], label="lower drone") + plt.xlabel("Time (s)") + plt.ylabel("z position (m)") + plt.legend() + plt.show() + + +if __name__ == "__main__": + main() + From a9e7a5d5265362a319e0b1adbe6d6c785ef90277 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Wed, 23 Sep 2026 17:55:21 +0200 Subject: [PATCH 02/14] Reformulates downwash as force on the individual rotor blades. Generates torques as well --- examples/plugins/downwash.py | 156 +++++++++++++++++++++-------------- 1 file changed, 94 insertions(+), 62 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 1f2e34e5..4c71ade6 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -1,123 +1,147 @@ -"""Minimal far-field downwash thrust-loss plugin. +"""Minimal far-field downwash external-wrench plugin. This models the downwash of level, hovering, identical Crazyflies using the -far-field jet from Bauersfeld et al. (arXiv:2403.13321). It belongs after -``force_torque_controller`` and before ``clip_rotor_vel_cmd``. +far-field jet from Bauersfeld et al. (arXiv:2403.13321) and the thrust-decay +model of Su et al. (arXiv:2207.09645). """ from __future__ import annotations from typing import TYPE_CHECKING -import jax import jax.numpy as jnp import numpy as np +from jax.scipy.spatial.transform import Rotation as R -from crazyflow.control.mellinger import force_torque2rotor_vel +from crazyflow.control.transform import motor_force2rotor_vel +from crazyflow.sim import Sim from crazyflow.sim.pipeline import insert_fn_before if TYPE_CHECKING: - from crazyflow.sim import Sim from crazyflow.sim.data import SimData # Physical parameters for the cf21B_500 AIR_DENSITY = 1.225 # kg/m^3 PROPELLER_RADIUS = 27.5e-3 # m -MOTOR_DISTANCE = 0.035355*2 # m, distance between opposite motors +MOTOR_DISTANCE = 0.035355 * 2 # m, distance between opposite motors N_PROPELLERS = 4 GRAVITY = 9.81 -# Far-field fit in Eq. (9) of the paper. +# This must be fitted for the propeller/downwash setup. +THRUST_DECAY_COEFFICIENT = 0.05 # s/m + +# Far-field fit in Eq. (9) of the Bauersfeld paper. BD = 10.11 S = 0.07668 S0 = -5.817 -def _thrust_loss(alpha: jax.Array) -> jax.Array: - """Return T_effective / T_nominal at constant aerodynamic power. +def downwash_fn(data: SimData) -> SimData: + """Apply downwash-induced thrust loss as a world-frame external wrench. - Equating the still-air and downwash momentum-theory powers yields the - positive root of eta**3 + alpha * eta - 1 = 0, with alpha = U_D / U_H. + The source flow originates at each drone centre, while the field is sampled + at every target rotor. """ - lower = jnp.zeros_like(alpha) - upper = jnp.ones_like(alpha) - - def bisect(_: int, bounds: tuple[jax.Array, jax.Array]) -> tuple[jax.Array, jax.Array]: - lower, upper = bounds - eta = (lower + upper) / 2.0 - above_root = eta**3 + alpha * eta > 1.0 - return jnp.where(above_root, lower, eta), jnp.where(above_root, eta, upper) - - lower, upper = jax.lax.fori_loop(0, 24, bisect, (lower, upper)) - return (lower + upper) / 2.0 - + rotation = R.from_quat(data.states.quat) + rotor_offsets = data.params.L * jnp.array( + [[1.0, -1.0, 0.0], [-1.0, -1.0, 0.0], [-1.0, 1.0, 0.0], [1.0, 1.0, 0.0]] + ) + rotor_offsets_world = jnp.swapaxes(rotation.as_matrix() @ rotor_offsets.T, -1, -2) + rotor_positions = data.states.pos[..., None, :] + rotor_offsets_world -def downwash_fn(data: SimData) -> SimData: - """Reduce every lower drone's nominal rotor force by its downwash loss.""" - # Axis 1 indexes the source drone; axis 2 indexes the target drone. - source_to_target = data.states.pos[:, :, None, :] - data.states.pos[:, None, :, :] + # Axis 1 indexes the source drone, axis 2 the target, and axis 3 its rotor. + source_to_target = data.states.pos[:, :, None, None, :] - rotor_positions[:, None, :, :, :] s = source_to_target[..., 2] # Positive only for targets below a source. r = jnp.linalg.vector_norm(source_to_target[..., :2], axis=-1) s_normalized = s / MOTOR_DISTANCE - mass = data.params.mass[0] + mass = data.params.mass[0] u_hover = jnp.sqrt( - mass * GRAVITY - / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) + mass * GRAVITY / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) ) half_width = S * (s_normalized - S0) centerline_velocity = u_hover * BD / (s_normalized - S0) xi = (r / MOTOR_DISTANCE) / half_width u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 - u_downwash = jnp.where(s_normalized > 2.5, u_downwash, 0.0) - u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target. - - eta = _thrust_loss(u_downwash / u_hover) - force_torque = data.controls.force_torque - - # Scale only thrust - effective_thrust = force_torque.cmd[..., 0] * eta - - rotor_vel = force_torque2rotor_vel( - effective_thrust[..., None], force_torque.cmd[..., 1:], **force_torque.params + # u_downwash = jnp.where(s_normalized > 2.5, u_downwash, 0.0) + u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. + + # Eq. (5) in Su et al.: each motor loses a fraction b_v * U_D of its + # current thrust. Clamp this extrapolation so effective thrust is never + # negative outside the fitted range. + loss_fraction = jnp.clip(THRUST_DECAY_COEFFICIENT * u_downwash, 0.0, 1.0) + rotor_vel = data.states.rotor_vel + k0, k1, k2 = ( + data.params.rpm2thrust[..., 0], + data.params.rpm2thrust[..., 1], + data.params.rpm2thrust[..., 2], ) - return data.replace(controls=data.controls.replace(rotor_vel=rotor_vel)) - - -def install_downwash(sim: Sim) -> None: - """Add downwash after allocation and rebuild the compiled step function.""" - insert_fn_before(sim.step_pipeline, "clip_rotor_vel_cmd", downwash_fn) - sim.build_step_fn() + motor_thrust = k0 + k1 * rotor_vel + k2 * rotor_vel**2 + thrust_delta = -loss_fraction * motor_thrust + + # Map the per-motor force changes to a body-frame wrench, as in Eq. (7). + total_thrust_delta = jnp.sum(thrust_delta, axis=-1) + zeros = jnp.zeros_like(total_thrust_delta) + force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) + + lever = jnp.array([1.0, 1.0, 0.0]) + torque_body = (data.params.mixing_matrix @ (thrust_delta * data.params.L)[..., None])[ + ..., 0 + ] * lever + + # Account for the corresponding reaction-torque change about body z. + effective_motor_thrust = jnp.maximum(motor_thrust + thrust_delta, 0.0) + effective_rotor_vel = motor_force2rotor_vel(effective_motor_thrust, data.params.rpm2thrust) + c0, c1, c2 = ( + data.params.rpm2torque[..., 0], + data.params.rpm2torque[..., 1], + data.params.rpm2torque[..., 2], + ) + motor_torque = c0 + c1 * rotor_vel + c2 * rotor_vel**2 + effective_motor_torque = c0 + c1 * effective_rotor_vel + c2 * effective_rotor_vel**2 + reaction_torque_delta = effective_motor_torque - motor_torque + torque_body = torque_body + (data.params.mixing_matrix @ reaction_torque_delta[..., None])[ + ..., 0 + ] * jnp.array([0.0, 0.0, 1.0]) + + states = data.states.replace( + force=rotation.apply(force_body), torque=rotation.apply(torque_body) + ) + return data.replace(states=states) def main(plot: bool = True) -> None: """Hover drone 0 while drone 1 flies straight through its downwash.""" - from crazyflow.sim import Sim - sim = Sim(n_drones=2, drone="cf21B_500", control="state") - install_downwash(sim) - upper_pos = np.array([0.0, 0.0, 1.2]) - lower_start = np.array([-0.5, 0.0, 1.0]) + insert_fn_before(sim.step_pipeline, "integration", downwash_fn) + sim.build_step_fn() + + upper_pos = np.array([0.0, 0.0, 1.0]) + lower_start = np.array([-0.5, 0.0, 0.5]) sim.data = sim.data.replace( states=sim.data.states.replace(pos=jnp.array([[upper_pos, lower_start]])) ) sim.build_default_data() - duration = 3.0 + duration = 6.0 speed = 1.0 / duration command = np.zeros((1, 2, 16)) command[..., 9:13] = [0.0, 0.0, 0.0, 1.0] # level quaternion (xyzw) command[0, 0, :3] = upper_pos z_positions = [] + downwash_force_z = [] + downwash_pitch_torque = [] for step in range(int(duration * sim.control_freq)): t = step / sim.control_freq - command[0, 1, :3] = [-0.5 + speed * t, 0.0, 1.0] + command[0, 1, :3] = [-0.5 + speed * t, 0.0, 0.5] command[0, 1, 3:6] = [speed, 0.0, 0.0] sim.state_control(command) sim.step(sim.freq // sim.control_freq) z_positions.append(np.asarray(sim.data.states.pos[0, :, 2])) + downwash_force_z.append(np.asarray(sim.data.states.force[0, 1, 2])) + downwash_pitch_torque.append(np.asarray(sim.data.states.torque[0, 1, 1])) sim.render() sim.close() @@ -126,14 +150,22 @@ def main(plot: bool = True) -> None: t = np.arange(len(z_positions)) / sim.control_freq z_positions = np.asarray(z_positions) - plt.plot(t, z_positions[:, 0], label="upper drone") - plt.plot(t, z_positions[:, 1], label="lower drone") - plt.xlabel("Time (s)") - plt.ylabel("z position (m)") - plt.legend() + fig, axes = plt.subplots(3, 1, sharex=True) + axes[0].plot(t, z_positions[:, 0], label="upper drone") + axes[0].plot(t, z_positions[:, 1], label="lower drone") + axes[0].set_ylabel("z position (m)") + axes[0].legend() + + axes[1].plot(t, downwash_force_z, label="lower drone") + axes[1].set_ylabel("downwash force z (N)") + axes[1].legend() + + axes[2].plot(t, downwash_pitch_torque, label="lower drone") + axes[2].set_xlabel("Time (s)") + axes[2].set_ylabel("downwash pitch torque y (Nm)") + axes[2].legend() plt.show() if __name__ == "__main__": main() - From baef4efb48c9b403e754aa87a09e491de3d0e378 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Thu, 24 Sep 2026 11:16:27 +0200 Subject: [PATCH 03/14] Adds plotting for downwash heatmap --- examples/plugins/downwash.py | 114 +++++++++++++++++++++++++++++------ 1 file changed, 96 insertions(+), 18 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 4c71ade6..991fb236 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -28,7 +28,7 @@ GRAVITY = 9.81 # This must be fitted for the propeller/downwash setup. -THRUST_DECAY_COEFFICIENT = 0.05 # s/m +THRUST_DECAY_COEFFICIENT = 0.07 # s/m # Far-field fit in Eq. (9) of the Bauersfeld paper. BD = 10.11 @@ -63,13 +63,13 @@ def downwash_fn(data: SimData) -> SimData: centerline_velocity = u_hover * BD / (s_normalized - S0) xi = (r / MOTOR_DISTANCE) / half_width u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 - # u_downwash = jnp.where(s_normalized > 2.5, u_downwash, 0.0) + + # This prevents "negative" downwash + u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. - # Eq. (5) in Su et al.: each motor loses a fraction b_v * U_D of its - # current thrust. Clamp this extrapolation so effective thrust is never - # negative outside the fitted range. - loss_fraction = jnp.clip(THRUST_DECAY_COEFFICIENT * u_downwash, 0.0, 1.0) + # Eq. (5) in Su et al.: each motor loses a fraction b_v * U_D of its current thrust + loss_fraction = THRUST_DECAY_COEFFICIENT * u_downwash rotor_vel = data.states.rotor_vel k0, k1, k2 = ( data.params.rpm2thrust[..., 0], @@ -109,48 +109,117 @@ def downwash_fn(data: SimData) -> SimData: ) return data.replace(states=states) +def plot_hover_velocity_field(source_positions: np.ndarray, mass: float) -> None: + """Plot the far-field downwash-speed magnitude in the y=0 plane.""" + import matplotlib.pyplot as plt + + x = np.linspace(-0.6, 0.6, 300) + z = np.linspace(0.0, 1.15, 300) + X, Z = np.meshgrid(x, z) + + # Every grid point lies in the y=0 plane. + points = np.stack((X, np.zeros_like(X), Z), axis=-1) + u_downwash = np.zeros_like(X) + + u_hover = np.sqrt( + mass * GRAVITY + / (2.0 * AIR_DENSITY * np.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) + ) + + for source_pos in source_positions: + source_to_point = source_pos - points + s = source_to_point[..., 2] + r = np.linalg.vector_norm(source_to_point[..., :2], axis=-1) + s_normalized = s / MOTOR_DISTANCE + + q = np.maximum(s_normalized - S0, 1e-6) + half_width = S * q + centerline_velocity = u_hover * BD / q + xi = (r / MOTOR_DISTANCE) / half_width + + velocity = centerline_velocity / (1.0 + (np.sqrt(2.0) - 1.0) * xi**2) ** 2 + u_downwash += velocity + + fig, ax = plt.subplots() + image = ax.pcolormesh(X, Z, u_downwash, shading="auto", cmap="viridis") + ax.scatter(source_positions[:, 0], source_positions[:, 2], color="red", label="source drone") + ax.set_xlabel("x (m)") + ax.set_ylabel("z (m)") + ax.set_title("Hovering-drone downwash speed") + ax.legend() + fig.colorbar(image, ax=ax, label="downward airspeed $U_D$ (m/s)") + plt.show() + def main(plot: bool = True) -> None: - """Hover drone 0 while drone 1 flies straight through its downwash.""" + """Hover drone 0 while drone 1 makes two downwash passes at different heights.""" sim = Sim(n_drones=2, drone="cf21B_500", control="state") insert_fn_before(sim.step_pipeline, "integration", downwash_fn) sim.build_step_fn() - upper_pos = np.array([0.0, 0.0, 1.0]) - lower_start = np.array([-0.5, 0.0, 0.5]) + upper_pos = np.array([0.0, 0.0, 1.2]) + outbound_height = 0.5 + return_height = 0.95 + lower_start = np.array([-0.5, 0.0, outbound_height]) + sim.data = sim.data.replace( states=sim.data.states.replace(pos=jnp.array([[upper_pos, lower_start]])) ) sim.build_default_data() - duration = 6.0 - speed = 1.0 / duration command = np.zeros((1, 2, 16)) - command[..., 9:13] = [0.0, 0.0, 0.0, 1.0] # level quaternion (xyzw) + command[..., 9:13] = [0.0, 0.0, 0.0, 1.0] command[0, 0, :3] = upper_pos + + waypoints = np.concatenate( + ( + np.linspace( + lower_start, + [0.5, 0.0, outbound_height], + 3 * sim.control_freq, + endpoint=False, + ), + np.linspace( + [0.5, 0.0, outbound_height], + [0.5, 0.0, return_height], + sim.control_freq, + endpoint=False, + ), + np.linspace( + [0.5, 0.0, return_height], + [-0.5, 0.0, return_height], + 3 * sim.control_freq, + ), + ) + ) + z_positions = [] downwash_force_z = [] downwash_pitch_torque = [] - for step in range(int(duration * sim.control_freq)): - t = step / sim.control_freq - command[0, 1, :3] = [-0.5 + speed * t, 0.0, 0.5] - command[0, 1, 3:6] = [speed, 0.0, 0.0] + for position in waypoints: + command[0, 1, :3] = position + command[0, 1, 3:6] = 0.0 # Position-only setpoints. + sim.state_control(command) sim.step(sim.freq // sim.control_freq) + z_positions.append(np.asarray(sim.data.states.pos[0, :, 2])) downwash_force_z.append(np.asarray(sim.data.states.force[0, 1, 2])) downwash_pitch_torque.append(np.asarray(sim.data.states.torque[0, 1, 1])) sim.render() sim.close() + if plot: import matplotlib.pyplot as plt - t = np.arange(len(z_positions)) / sim.control_freq + t = np.arange(len(waypoints)) / sim.control_freq z_positions = np.asarray(z_positions) + fig, axes = plt.subplots(3, 1, sharex=True) + axes[0].plot(t, z_positions[:, 0], label="upper drone") axes[0].plot(t, z_positions[:, 1], label="lower drone") axes[0].set_ylabel("z position (m)") @@ -161,9 +230,18 @@ def main(plot: bool = True) -> None: axes[1].legend() axes[2].plot(t, downwash_pitch_torque, label="lower drone") - axes[2].set_xlabel("Time (s)") + axes[2].set_xlabel("time (s)") axes[2].set_ylabel("downwash pitch torque y (Nm)") axes[2].legend() + + for axis in axes: + axis.axvline(3.0, color="black", linestyle="--", alpha=0.5) + axis.axvline(4.0, color="black", linestyle="--", alpha=0.5) + + plot_hover_velocity_field( + np.asarray([upper_pos]), + float(sim.data.params.mass[0]), + ) plt.show() From 5375c2c5a5006bfa1c404374cba420b6d4672157 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Fri, 25 Sep 2026 11:55:49 +0200 Subject: [PATCH 04/14] Downwash accounts now for relative tilt of the drone and other minor changes --- examples/plugins/downwash.py | 111 ++++++++++++++++++----------------- 1 file changed, 56 insertions(+), 55 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 991fb236..8361e830 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -1,8 +1,10 @@ """Minimal far-field downwash external-wrench plugin. -This models the downwash of level, hovering, identical Crazyflies using the -far-field jet from Bauersfeld et al. (arXiv:2403.13321) and the thrust-decay -model of Su et al. (arXiv:2207.09645). +This models the downwash of identical Crazyflies using the far-field jet from +[1] and the thrust-decay model of [2]. + +[1] Bauersfeld et al. https://arxiv.org/abs/2403.13321 +[2] Su et al. https://arxiv.org/abs/2207.09645 """ from __future__ import annotations @@ -13,7 +15,6 @@ import numpy as np from jax.scipy.spatial.transform import Rotation as R -from crazyflow.control.transform import motor_force2rotor_vel from crazyflow.sim import Sim from crazyflow.sim.pipeline import insert_fn_before @@ -23,14 +24,12 @@ # Physical parameters for the cf21B_500 AIR_DENSITY = 1.225 # kg/m^3 PROPELLER_RADIUS = 27.5e-3 # m -MOTOR_DISTANCE = 0.035355 * 2 # m, distance between opposite motors -N_PROPELLERS = 4 -GRAVITY = 9.81 +MOTOR_DISTANCE = 0.1 # m, distance between opposite motors # This must be fitted for the propeller/downwash setup. -THRUST_DECAY_COEFFICIENT = 0.07 # s/m +THRUST_DECAY_COEFFICIENT = 0.07 # s/m -# Far-field fit in Eq. (9) of the Bauersfeld paper. +# Far-field fit in Eq. (9) of [1] BD = 10.11 S = 0.07668 S0 = -5.817 @@ -40,35 +39,57 @@ def downwash_fn(data: SimData) -> SimData: """Apply downwash-induced thrust loss as a world-frame external wrench. The source flow originates at each drone centre, while the field is sampled - at every target rotor. + at every target rotor in the source's body frame. """ rotation = R.from_quat(data.states.quat) - rotor_offsets = data.params.L * jnp.array( - [[1.0, -1.0, 0.0], [-1.0, -1.0, 0.0], [-1.0, 1.0, 0.0], [1.0, 1.0, 0.0]] + mixing_matrix = data.params.mixing_matrix + + offsets = data.params.L * jnp.stack( + [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], + axis=0 ) - rotor_offsets_world = jnp.swapaxes(rotation.as_matrix() @ rotor_offsets.T, -1, -2) + rotor_offsets_body = offsets.T + rotor_offsets_world = jnp.swapaxes(rotation.as_matrix() @ rotor_offsets_body.T, -1, -2) rotor_positions = data.states.pos[..., None, :] + rotor_offsets_world # Axis 1 indexes the source drone, axis 2 the target, and axis 3 its rotor. source_to_target = data.states.pos[:, :, None, None, :] - rotor_positions[:, None, :, :, :] - s = source_to_target[..., 2] # Positive only for targets below a source. - r = jnp.linalg.vector_norm(source_to_target[..., :2], axis=-1) + # Rotate the source-minus-target displacement into each source's frame. + world_to_body = rotation.as_matrix().mT + # Broadcast each source rotation across all target drones and rotors. + source_to_target_body = ( + world_to_body[:, :, None, None, :, :] @ source_to_target[..., None] + )[..., 0] + s = source_to_target_body[..., 2] + r = jnp.linalg.vector_norm(source_to_target_body[..., :2], axis=-1) + + # Normalization according to [1] Eq. (8) s_normalized = s / MOTOR_DISTANCE + r_normalized = r / MOTOR_DISTANCE mass = data.params.mass[0] + gravity = -data.params.gravity_vec[2] + n_propellers = mixing_matrix.shape[-1] + u_hover = jnp.sqrt( - mass * GRAVITY / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) - ) - half_width = S * (s_normalized - S0) - centerline_velocity = u_hover * BD / (s_normalized - S0) - xi = (r / MOTOR_DISTANCE) / half_width - u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 + mass * gravity / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * n_propellers) + ) # [1] Eq. (1) + + # Keep the fit finite upstream, where its contribution is masked below. + axial_distance = jnp.maximum(s_normalized - S0, 1e-6) + half_width = S * axial_distance # [1] Eq. (6) + + centerline_velocity = u_hover * BD / axial_distance # [1] Eq. (2) + + xi = (r_normalized) / half_width # [1] Eq. (4) + + u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 # [1] Eq. (3) # This prevents "negative" downwash u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. - # Eq. (5) in Su et al.: each motor loses a fraction b_v * U_D of its current thrust + # [2] Eq. (5): each motor loses a fraction b_v * U_D of its current thrust loss_fraction = THRUST_DECAY_COEFFICIENT * u_downwash rotor_vel = data.states.rotor_vel k0, k1, k2 = ( @@ -79,37 +100,23 @@ def downwash_fn(data: SimData) -> SimData: motor_thrust = k0 + k1 * rotor_vel + k2 * rotor_vel**2 thrust_delta = -loss_fraction * motor_thrust - # Map the per-motor force changes to a body-frame wrench, as in Eq. (7). + # Map the per-motor force changes to a body-frame wrench, as in [2] Eq. (7). total_thrust_delta = jnp.sum(thrust_delta, axis=-1) zeros = jnp.zeros_like(total_thrust_delta) force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) lever = jnp.array([1.0, 1.0, 0.0]) - torque_body = (data.params.mixing_matrix @ (thrust_delta * data.params.L)[..., None])[ + torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[ ..., 0 ] * lever - # Account for the corresponding reaction-torque change about body z. - effective_motor_thrust = jnp.maximum(motor_thrust + thrust_delta, 0.0) - effective_rotor_vel = motor_force2rotor_vel(effective_motor_thrust, data.params.rpm2thrust) - c0, c1, c2 = ( - data.params.rpm2torque[..., 0], - data.params.rpm2torque[..., 1], - data.params.rpm2torque[..., 2], - ) - motor_torque = c0 + c1 * rotor_vel + c2 * rotor_vel**2 - effective_motor_torque = c0 + c1 * effective_rotor_vel + c2 * effective_rotor_vel**2 - reaction_torque_delta = effective_motor_torque - motor_torque - torque_body = torque_body + (data.params.mixing_matrix @ reaction_torque_delta[..., None])[ - ..., 0 - ] * jnp.array([0.0, 0.0, 1.0]) - states = data.states.replace( force=rotation.apply(force_body), torque=rotation.apply(torque_body) ) return data.replace(states=states) -def plot_hover_velocity_field(source_positions: np.ndarray, mass: float) -> None: + +def plot_hover_velocity_field(source_positions: np.ndarray, data: SimData) -> None: """Plot the far-field downwash-speed magnitude in the y=0 plane.""" import matplotlib.pyplot as plt @@ -121,9 +128,12 @@ def plot_hover_velocity_field(source_positions: np.ndarray, mass: float) -> None points = np.stack((X, np.zeros_like(X), Z), axis=-1) u_downwash = np.zeros_like(X) + gravity = -data.params.gravity_vec[2] + n_propellers = data.params.mixing_matrix.shape[-1] + mass = data.params.mass[0] + u_hover = np.sqrt( - mass * GRAVITY - / (2.0 * AIR_DENSITY * np.pi * PROPELLER_RADIUS**2 * N_PROPELLERS) + mass * gravity / (2.0 * AIR_DENSITY * np.pi * PROPELLER_RADIUS**2 * n_propellers) ) for source_pos in source_positions: @@ -169,16 +179,13 @@ def main(plot: bool = True) -> None: sim.build_default_data() command = np.zeros((1, 2, 16)) - command[..., 9:13] = [0.0, 0.0, 0.0, 1.0] + command[..., 9:13] = R.from_euler("z", 0).as_quat() command[0, 0, :3] = upper_pos waypoints = np.concatenate( ( np.linspace( - lower_start, - [0.5, 0.0, outbound_height], - 3 * sim.control_freq, - endpoint=False, + lower_start, [0.5, 0.0, outbound_height], 3 * sim.control_freq, endpoint=False ), np.linspace( [0.5, 0.0, outbound_height], @@ -187,9 +194,7 @@ def main(plot: bool = True) -> None: endpoint=False, ), np.linspace( - [0.5, 0.0, return_height], - [-0.5, 0.0, return_height], - 3 * sim.control_freq, + [0.5, 0.0, return_height], [-0.5, 0.0, return_height], 3 * sim.control_freq ), ) ) @@ -200,7 +205,6 @@ def main(plot: bool = True) -> None: for position in waypoints: command[0, 1, :3] = position - command[0, 1, 3:6] = 0.0 # Position-only setpoints. sim.state_control(command) sim.step(sim.freq // sim.control_freq) @@ -238,10 +242,7 @@ def main(plot: bool = True) -> None: axis.axvline(3.0, color="black", linestyle="--", alpha=0.5) axis.axvline(4.0, color="black", linestyle="--", alpha=0.5) - plot_hover_velocity_field( - np.asarray([upper_pos]), - float(sim.data.params.mass[0]), - ) + plot_hover_velocity_field(np.asarray([upper_pos]), sim.data) plt.show() From d20fb994804f1b5ac9760e58a4f49027fcf80f70 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Fri, 25 Sep 2026 12:19:03 +0200 Subject: [PATCH 05/14] Cleanes up rotation matrix logic --- examples/plugins/downwash.py | 22 +++++++++------------- 1 file changed, 9 insertions(+), 13 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 8361e830..bb32f174 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -1,7 +1,7 @@ """Minimal far-field downwash external-wrench plugin. This models the downwash of identical Crazyflies using the far-field jet from -[1] and the thrust-decay model of [2]. +[1] and the thrust-decay model of [2]. [1] Bauersfeld et al. https://arxiv.org/abs/2403.13321 [2] Su et al. https://arxiv.org/abs/2207.09645 @@ -41,24 +41,22 @@ def downwash_fn(data: SimData) -> SimData: The source flow originates at each drone centre, while the field is sampled at every target rotor in the source's body frame. """ - rotation = R.from_quat(data.states.quat) + R_body_to_world = R.from_quat(data.states.quat) + mixing_matrix = data.params.mixing_matrix offsets = data.params.L * jnp.stack( - [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], - axis=0 + [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], axis=0 ) - rotor_offsets_body = offsets.T - rotor_offsets_world = jnp.swapaxes(rotation.as_matrix() @ rotor_offsets_body.T, -1, -2) + rotor_offsets_world = (R_body_to_world.as_matrix() @ offsets).mT rotor_positions = data.states.pos[..., None, :] + rotor_offsets_world # Axis 1 indexes the source drone, axis 2 the target, and axis 3 its rotor. source_to_target = data.states.pos[:, :, None, None, :] - rotor_positions[:, None, :, :, :] - # Rotate the source-minus-target displacement into each source's frame. - world_to_body = rotation.as_matrix().mT + # Broadcast each source rotation across all target drones and rotors. source_to_target_body = ( - world_to_body[:, :, None, None, :, :] @ source_to_target[..., None] + R_body_to_world.as_matrix().mT[:, :, None, None, :, :] @ source_to_target[..., None] )[..., 0] s = source_to_target_body[..., 2] r = jnp.linalg.vector_norm(source_to_target_body[..., :2], axis=-1) @@ -106,12 +104,10 @@ def downwash_fn(data: SimData) -> SimData: force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) lever = jnp.array([1.0, 1.0, 0.0]) - torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[ - ..., 0 - ] * lever + torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[..., 0] * lever states = data.states.replace( - force=rotation.apply(force_body), torque=rotation.apply(torque_body) + force=R_body_to_world.apply(force_body), torque=R_body_to_world.apply(torque_body) ) return data.replace(states=states) From 4f23bd4d21d4c619aa96ee9a18f3b88c66e52dc1 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Tue, 29 Sep 2026 11:45:13 +0200 Subject: [PATCH 06/14] Uses .apply function to apply rotation --- examples/plugins/downwash.py | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index bb32f174..88be8156 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -41,23 +41,23 @@ def downwash_fn(data: SimData) -> SimData: The source flow originates at each drone centre, while the field is sampled at every target rotor in the source's body frame. """ - R_body_to_world = R.from_quat(data.states.quat) + R_world_to_body = R.from_quat(data.states.quat) mixing_matrix = data.params.mixing_matrix offsets = data.params.L * jnp.stack( - [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], axis=0 + [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], axis=-1 ) - rotor_offsets_world = (R_body_to_world.as_matrix() @ offsets).mT + rotor_offsets_world = R.from_quat(data.states.quat[..., None, :]).apply(offsets) rotor_positions = data.states.pos[..., None, :] + rotor_offsets_world # Axis 1 indexes the source drone, axis 2 the target, and axis 3 its rotor. source_to_target = data.states.pos[:, :, None, None, :] - rotor_positions[:, None, :, :, :] # Broadcast each source rotation across all target drones and rotors. - source_to_target_body = ( - R_body_to_world.as_matrix().mT[:, :, None, None, :, :] @ source_to_target[..., None] - )[..., 0] + source_to_target_body = R.from_quat(data.states.quat[..., None, None, :]).apply( + source_to_target, inverse=True + ) s = source_to_target_body[..., 2] r = jnp.linalg.vector_norm(source_to_target_body[..., :2], axis=-1) @@ -107,7 +107,7 @@ def downwash_fn(data: SimData) -> SimData: torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[..., 0] * lever states = data.states.replace( - force=R_body_to_world.apply(force_body), torque=R_body_to_world.apply(torque_body) + force=R_world_to_body.apply(force_body), torque=R_world_to_body.apply(torque_body) ) return data.replace(states=states) From 6d2f21af323280b9fa1d4ac9b68b219f2b56d9f0 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Tue, 29 Sep 2026 16:38:44 +0200 Subject: [PATCH 07/14] Adds scaling factor for tilt angle between source and target --- examples/plugins/downwash.py | 23 +++++++++++++++++------ 1 file changed, 17 insertions(+), 6 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 88be8156..aad6211c 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -85,6 +85,11 @@ def downwash_fn(data: SimData) -> SimData: # This prevents "negative" downwash u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) + + # Account for inclination between target drone and source field + z_axes = R_world_to_body.as_matrix()[..., :, 2] + cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) + u_downwash = u_downwash * cos_theta[..., None] u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. # [2] Eq. (5): each motor loses a fraction b_v * U_D of its current thrust @@ -100,6 +105,11 @@ def downwash_fn(data: SimData) -> SimData: # Map the per-motor force changes to a body-frame wrench, as in [2] Eq. (7). total_thrust_delta = jnp.sum(thrust_delta, axis=-1) + + # Account for inclination between target drone and source field + z_axes = R_world_to_body.as_matrix()[..., :, 2] + cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) + zeros = jnp.zeros_like(total_thrust_delta) force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) @@ -181,17 +191,18 @@ def main(plot: bool = True) -> None: waypoints = np.concatenate( ( np.linspace( - lower_start, [0.5, 0.0, outbound_height], 3 * sim.control_freq, endpoint=False + lower_start, [0.3, 0.0, outbound_height], 3 * sim.control_freq, endpoint=False ), + np.tile([0.3, 0.0, outbound_height], (2 * sim.control_freq, 1)), + np.linspace([0.3, 0.0, outbound_height], lower_start, int(0.5 * sim.control_freq)), + np.tile(lower_start, (2 * sim.control_freq, 1)), + np.linspace(lower_start, [-0.5, 0.0, return_height], sim.control_freq, endpoint=False), np.linspace( - [0.5, 0.0, outbound_height], + [-0.5, 0.0, return_height], [0.5, 0.0, return_height], - sim.control_freq, + 3 * sim.control_freq, endpoint=False, ), - np.linspace( - [0.5, 0.0, return_height], [-0.5, 0.0, return_height], 3 * sim.control_freq - ), ) ) From bd12101ff458e6dcb3ab5931b07e653d07345c38 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Tue, 29 Sep 2026 17:08:40 +0200 Subject: [PATCH 08/14] Adds drag model --- examples/plugins/downwash.py | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index aad6211c..ce8bfae3 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -44,6 +44,7 @@ def downwash_fn(data: SimData) -> SimData: R_world_to_body = R.from_quat(data.states.quat) mixing_matrix = data.params.mixing_matrix + drag_matrix = data.params.drag_matrix offsets = data.params.L * jnp.stack( [-mixing_matrix[1], mixing_matrix[0], jnp.zeros_like(mixing_matrix[0])], axis=-1 @@ -89,6 +90,14 @@ def downwash_fn(data: SimData) -> SimData: # Account for inclination between target drone and source field z_axes = R_world_to_body.as_matrix()[..., :, 2] cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) + + # Wind at each target rotor summed over sources + rotor_wind_world = jnp.sum(-u_downwash[..., None] * z_axes[:, :, None, None, :], axis=1) + + # Rotor-averaged wind representing the flow at the target CoM. + wind_com_world = jnp.mean(rotor_wind_world, axis=2) + wind_com_body = R_world_to_body.apply(wind_com_world, inverse=True) + u_downwash = u_downwash * cos_theta[..., None] u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. @@ -113,6 +122,10 @@ def downwash_fn(data: SimData) -> SimData: zeros = jnp.zeros_like(total_thrust_delta) force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) + # Compute drag induced through downwash + drag_body = (-drag_matrix @ wind_com_body[..., None])[..., 0] + force_body += drag_body + lever = jnp.array([1.0, 1.0, 0.0]) torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[..., 0] * lever From e09fd5355420399de58cbcc9ff87fda11d3baa94 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Tue, 29 Sep 2026 17:22:36 +0200 Subject: [PATCH 09/14] Removes lines from plotting --- examples/plugins/downwash.py | 4 ---- 1 file changed, 4 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index ce8bfae3..e0e0b1df 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -258,10 +258,6 @@ def main(plot: bool = True) -> None: axes[2].set_ylabel("downwash pitch torque y (Nm)") axes[2].legend() - for axis in axes: - axis.axvline(3.0, color="black", linestyle="--", alpha=0.5) - axis.axvline(4.0, color="black", linestyle="--", alpha=0.5) - plot_hover_velocity_field(np.asarray([upper_pos]), sim.data) plt.show() From a35ca03f8f7865bf95248926b0d0929ccc7a1eb3 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Tue, 29 Sep 2026 17:36:30 +0200 Subject: [PATCH 10/14] Adds an additional sample point for the downwash field at the drone COM for accurate computation of the local wind velocity vector --- examples/plugins/downwash.py | 26 +++++++++++--------------- 1 file changed, 11 insertions(+), 15 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index e0e0b1df..0f82df2c 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -39,7 +39,7 @@ def downwash_fn(data: SimData) -> SimData: """Apply downwash-induced thrust loss as a world-frame external wrench. The source flow originates at each drone centre, while the field is sampled - at every target rotor in the source's body frame. + at every target rotor and CoM in the source's body frame. """ R_world_to_body = R.from_quat(data.states.quat) @@ -52,10 +52,12 @@ def downwash_fn(data: SimData) -> SimData: rotor_offsets_world = R.from_quat(data.states.quat[..., None, :]).apply(offsets) rotor_positions = data.states.pos[..., None, :] + rotor_offsets_world - # Axis 1 indexes the source drone, axis 2 the target, and axis 3 its rotor. - source_to_target = data.states.pos[:, :, None, None, :] - rotor_positions[:, None, :, :, :] + sample_positions = jnp.concatenate([rotor_positions, data.states.pos[..., None, :]], axis=2) - # Broadcast each source rotation across all target drones and rotors. + # Axis 1 indexes the source, axis 2 the target, and axis 3 its rotors then CoM. + source_to_target = data.states.pos[:, :, None, None, :] - sample_positions[:, None, :, :, :] + + # Broadcast each source rotation across all target drones and sampling points. source_to_target_body = R.from_quat(data.states.quat[..., None, None, :]).apply( source_to_target, inverse=True ) @@ -87,17 +89,15 @@ def downwash_fn(data: SimData) -> SimData: # This prevents "negative" downwash u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) - # Account for inclination between target drone and source field z_axes = R_world_to_body.as_matrix()[..., :, 2] - cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) - # Wind at each target rotor summed over sources - rotor_wind_world = jnp.sum(-u_downwash[..., None] * z_axes[:, :, None, None, :], axis=1) - - # Rotor-averaged wind representing the flow at the target CoM. - wind_com_world = jnp.mean(rotor_wind_world, axis=2) + # The final sample is the CoM; each source's wind follows its negative z-axis. + wind_com_world = jnp.sum(-u_downwash[..., -1, None] * z_axes[:, :, None, :], axis=1) wind_com_body = R_world_to_body.apply(wind_com_world, inverse=True) + # Project only the rotor samples onto the target axis for thrust loss. + u_downwash = u_downwash[..., :-1] + cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) u_downwash = u_downwash * cos_theta[..., None] u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. @@ -115,10 +115,6 @@ def downwash_fn(data: SimData) -> SimData: # Map the per-motor force changes to a body-frame wrench, as in [2] Eq. (7). total_thrust_delta = jnp.sum(thrust_delta, axis=-1) - # Account for inclination between target drone and source field - z_axes = R_world_to_body.as_matrix()[..., :, 2] - cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) - zeros = jnp.zeros_like(total_thrust_delta) force_body = jnp.stack((zeros, zeros, total_thrust_delta), axis=-1) From 8562140f96e61c66b9d7c3df014b8b8fc5fec8d7 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Wed, 30 Sep 2026 10:42:33 +0200 Subject: [PATCH 11/14] Makes docs clearer --- examples/plugins/downwash.py | 34 ++++++++++++++++++++-------------- 1 file changed, 20 insertions(+), 14 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 0f82df2c..6ea38799 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -36,7 +36,7 @@ def downwash_fn(data: SimData) -> SimData: - """Apply downwash-induced thrust loss as a world-frame external wrench. + """Apply downwash-induced thrust loss and drag as a world-frame external wrench. The source flow originates at each drone centre, while the field is sampled at every target rotor and CoM in the source's body frame. @@ -89,7 +89,7 @@ def downwash_fn(data: SimData) -> SimData: # This prevents "negative" downwash u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) - z_axes = R_world_to_body.as_matrix()[..., :, 2] + z_axes = R_world_to_body.as_matrix()[..., 2] # The final sample is the CoM; each source's wind follows its negative z-axis. wind_com_world = jnp.sum(-u_downwash[..., -1, None] * z_axes[:, :, None, :], axis=1) @@ -122,6 +122,7 @@ def downwash_fn(data: SimData) -> SimData: drag_body = (-drag_matrix @ wind_com_body[..., None])[..., 0] force_body += drag_body + # Compute the torque generated by downwash lever = jnp.array([1.0, 1.0, 0.0]) torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[..., 0] * lever @@ -177,16 +178,16 @@ def plot_hover_velocity_field(source_positions: np.ndarray, data: SimData) -> No def main(plot: bool = True) -> None: - """Hover drone 0 while drone 1 makes two downwash passes at different heights.""" + """Hover drone 0 while drone 1 makes three downwash passes at different height and velocity.""" sim = Sim(n_drones=2, drone="cf21B_500", control="state") insert_fn_before(sim.step_pipeline, "integration", downwash_fn) sim.build_step_fn() upper_pos = np.array([0.0, 0.0, 1.2]) - outbound_height = 0.5 - return_height = 0.95 - lower_start = np.array([-0.5, 0.0, outbound_height]) + first_run_height = 0.5 + second_run_height = 0.95 + lower_start = np.array([-0.5, 0.0, first_run_height]) sim.data = sim.data.replace( states=sim.data.states.replace(pos=jnp.array([[upper_pos, lower_start]])) @@ -199,18 +200,23 @@ def main(plot: bool = True) -> None: waypoints = np.concatenate( ( + # First pass slow np.linspace( - lower_start, [0.3, 0.0, outbound_height], 3 * sim.control_freq, endpoint=False + lower_start, [0.3, 0.0, first_run_height], 3 * sim.control_freq, endpoint=False ), - np.tile([0.3, 0.0, outbound_height], (2 * sim.control_freq, 1)), - np.linspace([0.3, 0.0, outbound_height], lower_start, int(0.5 * sim.control_freq)), + # Pause to stabilize + np.tile([0.3, 0.0, first_run_height], (2 * sim.control_freq, 1)), + # Second pass fast + np.linspace([0.3, 0.0, first_run_height], lower_start, int(0.5 * sim.control_freq)), + # Pause to stabilize np.tile(lower_start, (2 * sim.control_freq, 1)), - np.linspace(lower_start, [-0.5, 0.0, return_height], sim.control_freq, endpoint=False), + # Increase altitude np.linspace( - [-0.5, 0.0, return_height], - [0.5, 0.0, return_height], - 3 * sim.control_freq, - endpoint=False, + lower_start, [-0.5, 0.0, second_run_height], sim.control_freq, endpoint=False + ), + # Third pass closer to hovering drone + np.linspace( + [-0.5, 0.0, second_run_height], [0.5, 0.0, second_run_height], 3 * sim.control_freq ), ) ) From 4b32a459608c2de120dcb86fea941ee572dbf129 Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Wed, 30 Sep 2026 14:01:40 +0200 Subject: [PATCH 12/14] Adds docs with media --- docs/examples/index.md | 21 +++++++++++++++++++++ docs/img/examples/downwash_example.gif | Bin 0 -> 1964525 bytes docs/img/examples/downwash_field.png | Bin 0 -> 42906 bytes docs/user-guide/pipelines.md | 2 ++ examples/plugins/downwash.py | 13 ++++++++----- 5 files changed, 31 insertions(+), 5 deletions(-) create mode 100644 docs/img/examples/downwash_example.gif create mode 100644 docs/img/examples/downwash_field.png diff --git a/docs/examples/index.md b/docs/examples/index.md index fc6a7913..7c6452da 100644 --- a/docs/examples/index.md +++ b/docs/examples/index.md @@ -110,6 +110,27 @@ Inserting a random external force and torque into the step pipeline. The disturb --- +## Downwash + +Modeling downwash between identical Crazyflies with a far-field jet model. The plugin samples the flow at each target rotor and center of mass, computes rotor thrust loss and drag, and writes the resulting world-frame external force and torque. + +The demo holds one `cf21B_500` drone in hover while a second makes three passes underneath at different speeds and heights. + +
+
+ Drone flying through downwash cone +
+
+ Downwash field generated by hovering drone +
+
+ +```bash +python examples/plugins/downwash.py +``` + +--- + ## Cameras and RGBD Offscreen rendering returns RGB-D images on every frame. 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velocity = centerline_velocity / (1.0 + (np.sqrt(2.0) - 1.0) * xi**2) ** 2 u_downwash += velocity - fig, ax = plt.subplots() + fig, ax = plt.subplots(figsize=(6, 4.5), layout="constrained") image = ax.pcolormesh(X, Z, u_downwash, shading="auto", cmap="viridis") ax.scatter(source_positions[:, 0], source_positions[:, 2], color="red", label="source drone") - ax.set_xlabel("x (m)") - ax.set_ylabel("z (m)") - ax.set_title("Hovering-drone downwash speed") + ax.set_xlabel("x (m)", fontsize=14) + ax.set_ylabel("z (m)", fontsize=14) + ax.tick_params(axis="both", labelsize=12) + ax.set_title("Hovering-drone downwash speed", fontsize=14) ax.legend() - fig.colorbar(image, ax=ax, label="downward airspeed $U_D$ (m/s)") + colorbar = fig.colorbar(image, ax=ax, pad=0.02) + colorbar.set_label("downward airspeed $U_D$ (m/s)", fontsize=14) + colorbar.ax.tick_params(labelsize=12) plt.show() From 0e455c747d7aae390222067769a2c77f6c9c61eb Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Wed, 30 Sep 2026 15:03:33 +0200 Subject: [PATCH 13/14] Outsource downwash speed computation at sample points --- examples/plugins/downwash.py | 68 ++++++++++++++++++------------------ 1 file changed, 34 insertions(+), 34 deletions(-) diff --git a/examples/plugins/downwash.py b/examples/plugins/downwash.py index 203c6f10..e522c9e3 100644 --- a/examples/plugins/downwash.py +++ b/examples/plugins/downwash.py @@ -19,6 +19,8 @@ from crazyflow.sim.pipeline import insert_fn_before if TYPE_CHECKING: + from jax import Array + from crazyflow.sim.data import SimData # Physical parameters for the cf21B_500 @@ -35,13 +37,34 @@ S0 = -5.817 +def downwash_speed(s: Array, r: Array, u_hover: Array) -> Array: + """Return downwash speed at axial and radial distances in metres. + + Positive s points downstream along the source drone's negative body z-axis. + Inputs broadcast to the sampling grid; the returned speeds are in m/s. + """ + # Normalization according to [1] Eq. (8). + s_normalized = s / MOTOR_DISTANCE + r_normalized = r / MOTOR_DISTANCE + + # Keep the fit finite upstream, where its contribution is masked below. + axial_distance = jnp.maximum(s_normalized - S0, 1e-6) + half_width = S * axial_distance # [1] Eq. (6) + centerline_speed = u_hover * BD / axial_distance # [1] Eq. (2) + radial_ratio = r_normalized / half_width # [1] Eq. (4) + + # [1] Eq. (3). + speed = centerline_speed / (1.0 + (jnp.sqrt(2.0) - 1.0) * radial_ratio**2) ** 2 + return jnp.where(s_normalized > 0.1, speed, 0.0) + + def downwash_fn(data: SimData) -> SimData: """Apply downwash-induced thrust loss and drag as a world-frame external wrench. The source flow originates at each drone centre, while the field is sampled at every target rotor and CoM in the source's body frame. """ - R_world_to_body = R.from_quat(data.states.quat) + body_to_world = R.from_quat(data.states.quat) mixing_matrix = data.params.mixing_matrix drag_matrix = data.params.drag_matrix @@ -64,10 +87,6 @@ def downwash_fn(data: SimData) -> SimData: s = source_to_target_body[..., 2] r = jnp.linalg.vector_norm(source_to_target_body[..., :2], axis=-1) - # Normalization according to [1] Eq. (8) - s_normalized = s / MOTOR_DISTANCE - r_normalized = r / MOTOR_DISTANCE - mass = data.params.mass[0] gravity = -data.params.gravity_vec[2] n_propellers = mixing_matrix.shape[-1] @@ -76,33 +95,22 @@ def downwash_fn(data: SimData) -> SimData: mass * gravity / (2.0 * AIR_DENSITY * jnp.pi * PROPELLER_RADIUS**2 * n_propellers) ) # [1] Eq. (1) - # Keep the fit finite upstream, where its contribution is masked below. - axial_distance = jnp.maximum(s_normalized - S0, 1e-6) - half_width = S * axial_distance # [1] Eq. (6) - - centerline_velocity = u_hover * BD / axial_distance # [1] Eq. (2) - - xi = (r_normalized) / half_width # [1] Eq. (4) - - u_downwash = centerline_velocity / (1.0 + (jnp.sqrt(2.0) - 1.0) * xi**2) ** 2 # [1] Eq. (3) + # Shape: (world, source, target, sample), with rotors followed by the CoM. + sample_speed = downwash_speed(s, r, u_hover) - # This prevents "negative" downwash - u_downwash = jnp.where(s_normalized > 0.1, u_downwash, 0.0) - - z_axes = R_world_to_body.as_matrix()[..., 2] + z_axes = body_to_world.as_matrix()[..., 2] # The final sample is the CoM; each source's wind follows its negative z-axis. - wind_com_world = jnp.sum(-u_downwash[..., -1, None] * z_axes[:, :, None, :], axis=1) - wind_com_body = R_world_to_body.apply(wind_com_world, inverse=True) + wind_com_world = jnp.sum(-sample_speed[..., -1, None] * z_axes[:, :, None, :], axis=1) + wind_com_body = body_to_world.apply(wind_com_world, inverse=True) # Project only the rotor samples onto the target axis for thrust loss. - u_downwash = u_downwash[..., :-1] cos_theta = jnp.sum(z_axes[:, :, None, :] * z_axes[:, None, :, :], axis=-1) - u_downwash = u_downwash * cos_theta[..., None] - u_downwash = jnp.sum(u_downwash, axis=1) # Sum all sources at each target rotor. + # Sum all sources at each target rotor: (world, target, rotor). + rotor_inflow = jnp.sum(sample_speed[..., :-1] * cos_theta[..., None], axis=1) # [2] Eq. (5): each motor loses a fraction b_v * U_D of its current thrust - loss_fraction = THRUST_DECAY_COEFFICIENT * u_downwash + loss_fraction = THRUST_DECAY_COEFFICIENT * rotor_inflow rotor_vel = data.states.rotor_vel k0, k1, k2 = ( data.params.rpm2thrust[..., 0], @@ -127,7 +135,7 @@ def downwash_fn(data: SimData) -> SimData: torque_body = (mixing_matrix @ (thrust_delta * data.params.L)[..., None])[..., 0] * lever states = data.states.replace( - force=R_world_to_body.apply(force_body), torque=R_world_to_body.apply(torque_body) + force=body_to_world.apply(force_body), torque=body_to_world.apply(torque_body) ) return data.replace(states=states) @@ -156,15 +164,7 @@ def plot_hover_velocity_field(source_positions: np.ndarray, data: SimData) -> No source_to_point = source_pos - points s = source_to_point[..., 2] r = np.linalg.vector_norm(source_to_point[..., :2], axis=-1) - s_normalized = s / MOTOR_DISTANCE - - q = np.maximum(s_normalized - S0, 1e-6) - half_width = S * q - centerline_velocity = u_hover * BD / q - xi = (r / MOTOR_DISTANCE) / half_width - - velocity = centerline_velocity / (1.0 + (np.sqrt(2.0) - 1.0) * xi**2) ** 2 - u_downwash += velocity + u_downwash += np.asarray(downwash_speed(jnp.asarray(s), jnp.asarray(r), u_hover)) fig, ax = plt.subplots(figsize=(6, 4.5), layout="constrained") image = ax.pcolormesh(X, Z, u_downwash, shading="auto", cmap="viridis") From cb13a1e85fba8efae6f712a49c7236c3ae45613e Mon Sep 17 00:00:00 2001 From: radu_workstation Date: Wed, 30 Sep 2026 15:17:52 +0200 Subject: [PATCH 14/14] Adds ground effect docs. Refines pipelines part --- docs/examples/index.md | 15 +++++++++++++++ docs/user-guide/pipelines.md | 3 +-- 2 files changed, 16 insertions(+), 2 deletions(-) diff --git a/docs/examples/index.md b/docs/examples/index.md index 7c6452da..66dab31f 100644 --- a/docs/examples/index.md +++ b/docs/examples/index.md @@ -131,6 +131,21 @@ python examples/plugins/downwash.py --- +## Ground effect + +Modeling the increase in thrust near the floor for a `cf21B_500` drone. The plugin computes nominal thrust from the rotor speeds, applies a height-dependent gain, and adds the extra thrust along the drone's body z-axis as a world-frame external force. + + +```{ .python notest } +--8<-- "examples/plugins/ground_effect.py" +``` + +```bash +python examples/plugins/ground_effect.py +``` + +--- + ## Cameras and RGBD Offscreen rendering returns RGB-D images on every frame. The FPV camera (`fpv_cam`) is attached to the drone and moves with it. diff --git a/docs/user-guide/pipelines.md b/docs/user-guide/pipelines.md index 2644bce9..6aaa73b3 100644 --- a/docs/user-guide/pipelines.md +++ b/docs/user-guide/pipelines.md @@ -237,8 +237,7 @@ sim.step() See the [disturbance injection example](../examples/index.md#disturbance-injection) for a full run comparing disturbed and undisturbed trajectories. -The [downwash example](../examples/index.md#downwash) uses the same insertion point to model interactions between drones. It samples a far-field flow model at each drone's rotors and center of mass, then applies thrust loss and drag through the external force and torque fields. - +Aerodynamic effects such as [downwash](../examples/index.md#downwash) and [ground effect](../examples/index.md#ground-effect) use the same approach: insert a stage before `integration` that updates the external force or torque fields. ## Next steps