backend sim: pinocchio (#408)

* Add pinoccio backend for simulation

crazyflie_sim/crazyflie_sim/backend/data/pinocchio/crazyflie2.urdf

@@ -0,0 +1,27 @@
+<?xml version="1.0"?>
+<robot name="crazflie">
+
+    <link name="world"></link>
+
+    <joint name="freefly" type="floating">
+        <parent link="world"/>
+        <child link="base"/>
+        <axis xyz="1 1 1"/>
+        <limit effort="1000.0" lower="-100.0" upper="100.0" velocity="100.0"/>
+    </joint>
+
+    <link name="base">
+        <inertial>
+            <mass value="0.034"/>
+            <origin xyz="0 0 0"/>
+            <inertia ixx="16.571710e-6" iyy="16.655602e-6" izz="29.261652e-6" ixy="0.0" ixz="0.0" iyx="0.0" iyz="0.0" izx="0.0" izy="0.0"/>
+        </inertial>
+
+        <collision>
+            <origin rpy="0 0 0" xyz="0 0 0"/>
+            <geometry>
+                <sphere radius="0.1"/>
+            </geometry>
+        </collision>      
+    </link>
+</robot>

crazyflie_sim/crazyflie_sim/backend/pinocchio.py

@@ -0,0 +1,118 @@
+from pathlib import Path
+
+import numpy as np
+import pinocchio as pin
+from rclpy.node import Node
+from rclpy.time import Time
+from rosgraph_msgs.msg import Clock
+
+from ..sim_data_types import Action, State
+
+
+class Backend:
+    """Backend that uses pinocchio to simulate the rigid-body dynamics."""
+
+    def __init__(self, node: Node, names: list[str], states: list[State]):
+        self.node = node
+        self.names = names
+        self.clock_publisher = node.create_publisher(Clock, 'clock', 10)
+        self.t = 0
+        self.dt = 0.0005
+
+        self.uavs = []
+        for state in states:
+            uav = Quadrotor(state)
+            self.uavs.append(uav)
+
+    def time(self) -> float:
+        return self.t
+
+    def step(self, states_desired: list[State], actions: list[Action]) -> list[State]:
+        # advance the time
+        self.t += self.dt
+
+        next_states = []
+
+        for uav, action in zip(self.uavs, actions):
+            uav.step(action, self.dt)
+            next_states.append(uav.state)
+
+        # print(states_desired, actions, next_states)
+        # publish the current clock
+        clock_message = Clock()
+        clock_message.clock = Time(seconds=self.time()).to_msg()
+        self.clock_publisher.publish(clock_message)
+
+        return next_states
+
+    def shutdown(self):
+        pass
+
+
+# convert RPM -> Force
+def rpm_to_force(rpm):
+    # polyfit using data and scripts from https://github.com/IMRCLab/crazyflie-system-id
+    p = [2.55077341e-08, -4.92422570e-05, -1.51910248e-01]
+    force_in_grams = np.polyval(p, rpm)
+    force_in_newton = force_in_grams * 9.81 / 1000.0
+    return np.maximum(force_in_newton, 0)
+
+
+def pinocchio_state2sim_state(q, v):
+    result = State()
+    result.pos = q[0:3]
+    result.quat = np.concatenate((q[6:7], q[3:6]))
+    result.vel = v[0:3]
+    result.omega = v[3:6]
+    return result
+
+
+def sim_state2pinocchio_state(state):
+    result = np.empty(13)
+    result[0:3] = state.pos
+    result[3:6] = state.quat[1:]
+    result[6] = state.quat[0]
+    result[7:10] = state.vel
+    result[10:13] = state.omega
+    q = result[0:7]  # geometric states: x, y, z, qx, qy, qz, qw
+    v = result[7:]  # velocities: vx, vy, vz, wx, wy, wz
+    return q, v
+
+
+class Quadrotor:
+    """Basic rigid body quadrotor model (no drag) using numpy and rowan."""
+
+    def __init__(self, state):
+        arm_length = 0.046  # m
+        arm = 0.707106781 * arm_length
+        t2t = 0.006  # thrust-to-torque ratio
+        self.B0 = np.array([
+            [1, 1, 1, 1],
+            [-arm, -arm, arm, arm],
+            [-arm, arm, arm, -arm],
+            [-t2t, t2t, -t2t, t2t]
+            ])
+        self.uav, self.collision_model, self.visual_model = pin.buildModelsFromUrdf(
+            str((Path(__file__).parent / 'data/pinocchio/crazyflie2.urdf')))
+        self.uavPinocchioData = self.uav.createData()
+        self.state = state
+
+    def step(self, action, dt):
+
+        # m: 0.034
+        # max_f: 1.3
+        force_in_newton = rpm_to_force(action.rpm)
+        eta = np.dot(self.B0, force_in_newton)
+        force_generalized = np.array([0., 0., eta[0], eta[1], eta[2], eta[3]])
+
+        q, v = sim_state2pinocchio_state(self.state)
+        a = pin.aba(self.uav, self.uavPinocchioData, q, v, force_generalized)
+        v_next = v + a*dt
+        q_next = pin.integrate(self.uav, q, v*dt)
+        self.state = pinocchio_state2sim_state(q_next, v_next)
+
+        # if we fall below the ground, set velocities to 0
+        if self.state.pos[2] < 0:
+            self.state.pos[2] = 0
+            self.state.vel = [0, 0, 0]
+            self.state.omega = [0, 0, 0]