Johnny Fernandes
191 lines
6.9 KiB
Python
191 lines
6.9 KiB
Python
"""Differential-drive and mecanum kinematics, shared by the env and Webots
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controllers.
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First-order rigid-body model — no slip, wheel-accel limits, or contact
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forces. Webots' ODE physics handles those at inference; the env stays
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close enough to first order that a policy trained here transfers.
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"""
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import math
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def kinematics_step(x, y, h, w_left, w_right, wheel_radius, wheel_base, dt):
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"""Integrate one step of differential-drive forward kinematics.
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Inputs
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------
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x, y : robot position (m)
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h : robot heading (rad), 0 = +x axis
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w_left, w_right : wheel angular velocities (rad/s)
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wheel_radius, wheel_base : robot dimensions (m)
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dt : timestep (s)
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Returns (new_x, new_y, new_h).
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"""
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v = (w_right + w_left) * wheel_radius * 0.5
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omega = (w_right - w_left) * wheel_radius / wheel_base
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new_x = x + v * math.cos(h) * dt
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new_y = y + v * math.sin(h) * dt
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new_h = math.atan2(math.sin(h + omega * dt), math.cos(h + omega * dt))
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return new_x, new_y, new_h
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def velocity_to_wheels(vx, vy, h, max_linear, wheel_radius, max_wheel_omega,
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k_turn=4.0):
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"""Convert a desired (vx, vy) intent in [-1, 1]² to wheel speeds.
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Forward speed scales by ``cos(err)`` (clamped to ±90°); a P
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controller on heading error contributes the wheel-rate differential.
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"""
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speed_ms = math.hypot(vx, vy) * max_linear
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if speed_ms < 1e-3:
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return 0.0, 0.0
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target_h = math.atan2(vy, vx)
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err = math.atan2(math.sin(target_h - h), math.cos(target_h - h))
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clamped_err = max(-math.pi / 2, min(math.pi / 2, err))
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fwd_ms = speed_ms * math.cos(clamped_err)
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fwd_rad = fwd_ms / wheel_radius
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turn = k_turn * err
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left = max(-max_wheel_omega, min(max_wheel_omega, fwd_rad - turn))
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right = max(-max_wheel_omega, min(max_wheel_omega, fwd_rad + turn))
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return left, right
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def heading_speed_to_wheels(heading, speed_motor, h, max_wheel_omega,
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k_turn=4.0):
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"""Sheep variant: speed in wheel rad/s, target as a heading angle."""
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err = math.atan2(math.sin(heading - h), math.cos(heading - h))
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fwd = max(0.0, math.cos(err)) * speed_motor
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turn = k_turn * err
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left = max(-max_wheel_omega, min(max_wheel_omega, fwd - turn))
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right = max(-max_wheel_omega, min(max_wheel_omega, fwd + turn))
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return left, right
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# ---------------------------------------------------------------------------
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# Mecanum (4-wheel omnidirectional) kinematics
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# ---------------------------------------------------------------------------
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def mecanum_kinematics_step(x, y, h, w_fl, w_fr, w_rl, w_rr,
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wheel_radius, lx, ly, dt):
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"""Integrate one step of mecanum forward kinematics.
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Parameters
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----------
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x, y : robot position (m)
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h : robot heading (rad), 0 = +x axis
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w_fl, w_fr, w_rl, w_rr : wheel angular velocities (rad/s)
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wheel_radius : wheel radius (m)
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lx : half the front-to-back axle distance (m)
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ly : half the left-to-right axle distance (m)
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dt : timestep (s)
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Returns (new_x, new_y, new_h).
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"""
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r = wheel_radius
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vx_body = (w_fl + w_fr + w_rl + w_rr) * r / 4.0
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vy_body = (-w_fl + w_fr + w_rl - w_rr) * r / 4.0
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omega = (-w_fl + w_fr - w_rl + w_rr) * r / (4.0 * (lx + ly))
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cos_h = math.cos(h)
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sin_h = math.sin(h)
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vx_world = vx_body * cos_h - vy_body * sin_h
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vy_world = vx_body * sin_h + vy_body * cos_h
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new_x = x + vx_world * dt
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new_y = y + vy_world * dt
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new_h = math.atan2(math.sin(h + omega * dt), math.cos(h + omega * dt))
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return new_x, new_y, new_h
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def mecanum_inverse(vx_body, vy_body, omega, wheel_radius, lx, ly,
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max_wheel_omega):
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"""Mecanum inverse kinematics: body-frame velocities to 4 wheel speeds.
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Parameters
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----------
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vx_body, vy_body : desired body-frame linear velocities (m/s)
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omega : desired yaw rate (rad/s)
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wheel_radius : wheel radius (m)
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lx : half front-to-back axle distance (m)
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ly : half left-to-right axle distance (m)
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max_wheel_omega : wheel angular velocity clamp (rad/s)
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Returns (w_fl, w_fr, w_rl, w_rr).
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"""
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r = wheel_radius
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k = lx + ly
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w_fl = (vx_body - vy_body - k * omega) / r
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w_fr = (vx_body + vy_body + k * omega) / r
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w_rl = (vx_body + vy_body - k * omega) / r
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w_rr = (vx_body - vy_body + k * omega) / r
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scale = max(abs(w_fl), abs(w_fr), abs(w_rl), abs(w_rr), 1e-9)
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if scale > max_wheel_omega:
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ratio = max_wheel_omega / scale
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w_fl *= ratio
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w_fr *= ratio
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w_rl *= ratio
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w_rr *= ratio
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return w_fl, w_fr, w_rl, w_rr
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def velocity_to_mecanum_wheels(vx, vy, omega, h, max_linear, wheel_radius,
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lx, ly, max_wheel_omega,
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k_turn=4.0, wheel_base=0.28):
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"""Convert world-frame (vx, vy, omega) action in [-1, 1]^3 to 4 wheel speeds.
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Truly holonomic interpretation: (vx, vy) is the desired *world-frame*
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velocity (magnitude up to ``max_linear`` m/s) and ``omega`` is the
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desired yaw rate (independent of motion direction). The dog can
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crab-walk and rotate at the same time.
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This matches the universal teacher's signal: drive toward a standoff
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point while facing the sheep / pen separately. With the older
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non-holonomic version, ``omega`` from the teacher fought against the
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forward-only kinematics and dropped success rates instead of helping.
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Parameters
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----------
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vx, vy : desired world-frame velocity intent in [-1, 1] (clamped on
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magnitude to ≤ 1)
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omega : desired yaw rate intent in [-1, 1]
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h : current heading (rad), 0 = +x
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max_linear : max linear speed (m/s)
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wheel_radius : wheel radius (m)
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lx, ly : half axle distances (m)
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max_wheel_omega : wheel angular velocity clamp (rad/s)
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k_turn : unused (kept for signature compatibility)
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wheel_base : unused (kept for signature compatibility)
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Returns (w_fl, w_fr, w_rl, w_rr).
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"""
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# Clamp the action magnitude in the (vx, vy) unit disk.
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norm = math.hypot(vx, vy)
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if norm > 1.0:
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vx /= norm
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vy /= norm
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# World-frame velocity → body-frame velocity (rotate by -h).
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vx_world = vx * max_linear
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vy_world = vy * max_linear
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cos_h = math.cos(h)
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sin_h = math.sin(h)
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vx_body = cos_h * vx_world + sin_h * vy_world
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vy_body = -sin_h * vx_world + cos_h * vy_world
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# Yaw rate: omega ∈ [-1, 1] maps to ± max_linear / (lx + ly) — same
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# peak yaw as the old "omega_extra" channel, but used directly
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# rather than added to a heading-tracker.
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yaw_max = max_linear / max(lx + ly, 1e-6)
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omega_rad = omega * yaw_max
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if abs(vx_body) < 1e-3 and abs(vy_body) < 1e-3 and abs(omega_rad) < 1e-3:
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return 0.0, 0.0, 0.0, 0.0
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return mecanum_inverse(
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vx_body, vy_body, omega_rad,
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wheel_radius, lx, ly, max_wheel_omega,
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)
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