Johnny Fernandes
62 lines
2.3 KiB
Python
62 lines
2.3 KiB
Python
"""Differential-drive kinematics, shared by the env and Webots controllers.
|
|
|
|
First-order rigid-body model — no slip, wheel-accel limits, or contact
|
|
forces. Webots' ODE physics handles those at inference; the env stays
|
|
close enough to first order that a policy trained here transfers.
|
|
"""
|
|
|
|
import math
|
|
|
|
|
|
def kinematics_step(x, y, h, w_left, w_right, wheel_radius, wheel_base, dt):
|
|
"""Integrate one step of differential-drive forward kinematics.
|
|
|
|
Inputs
|
|
------
|
|
x, y : robot position (m)
|
|
h : robot heading (rad), 0 = +x axis
|
|
w_left, w_right : wheel angular velocities (rad/s)
|
|
wheel_radius, wheel_base : robot dimensions (m)
|
|
dt : timestep (s)
|
|
|
|
Returns (new_x, new_y, new_h).
|
|
"""
|
|
v = (w_right + w_left) * wheel_radius * 0.5
|
|
omega = (w_right - w_left) * wheel_radius / wheel_base
|
|
new_x = x + v * math.cos(h) * dt
|
|
new_y = y + v * math.sin(h) * dt
|
|
new_h = math.atan2(math.sin(h + omega * dt), math.cos(h + omega * dt))
|
|
return new_x, new_y, new_h
|
|
|
|
|
|
def velocity_to_wheels(vx, vy, h, max_linear, wheel_radius, max_wheel_omega,
|
|
k_turn=4.0):
|
|
"""Convert a desired (vx, vy) intent in [-1, 1]² to wheel speeds.
|
|
|
|
Forward speed scales by ``cos(err)`` (clamped to ±90°); a P
|
|
controller on heading error contributes the wheel-rate differential.
|
|
"""
|
|
speed_ms = math.hypot(vx, vy) * max_linear
|
|
if speed_ms < 1e-3:
|
|
return 0.0, 0.0
|
|
target_h = math.atan2(vy, vx)
|
|
err = math.atan2(math.sin(target_h - h), math.cos(target_h - h))
|
|
clamped_err = max(-math.pi / 2, min(math.pi / 2, err))
|
|
fwd_ms = speed_ms * math.cos(clamped_err)
|
|
fwd_rad = fwd_ms / wheel_radius
|
|
turn = k_turn * err
|
|
left = max(-max_wheel_omega, min(max_wheel_omega, fwd_rad - turn))
|
|
right = max(-max_wheel_omega, min(max_wheel_omega, fwd_rad + turn))
|
|
return left, right
|
|
|
|
|
|
def heading_speed_to_wheels(heading, speed_motor, h, max_wheel_omega,
|
|
k_turn=4.0):
|
|
"""Sheep variant: speed in wheel rad/s, target as a heading angle."""
|
|
err = math.atan2(math.sin(heading - h), math.cos(heading - h))
|
|
fwd = max(0.0, math.cos(err)) * speed_motor
|
|
turn = k_turn * err
|
|
left = max(-max_wheel_omega, min(max_wheel_omega, fwd - turn))
|
|
right = max(-max_wheel_omega, min(max_wheel_omega, fwd + turn))
|
|
return left, right
|