Fault Environment Example

This tutorial demonstrates how to configure and use a simple BSK-RL environment to model faults in a system with four reaction wheels (RWs).

Load Modules

[1]:
import numpy as np
from typing import Iterable

from Basilisk.architecture import bskLogging
from Basilisk.utilities import macros, orbitalMotion, simIncludeRW
from Basilisk.simulation import reactionWheelStateEffector
from Basilisk.fswAlgorithms import rwNullSpace
from Basilisk.architecture import messaging
from bsk_rl import SatelliteTasking, act, data, obs, scene, sats
from bsk_rl.sim import dyn, fsw
from bsk_rl.utils.orbital import random_orbit, random_unit_vector
from bsk_rl.utils.functional import default_args

bskLogging.setDefaultLogLevel(bskLogging.BSK_WARNING)

Making Faults Cases

Creating a fault base class and defining individual fault types enables modeling multiple kinds of faults within a single satellite. In this example, a power draw limit is applied to RWs, causing it to operate at reduced speed compared to nominal conditions. By default, while a torque limit is enforced, there are no restrictions on power draw. time is used to define the time at which the fault occurs, reducedLimit specifies the power draw limit in watts, and wheel_Idx indicates which RW is affected by the fault. It can be set to a value from 1 to 4, or to all to apply the fault to every RW.

[2]:
class FaultObject:
    def __init__(self, name, time, verbose=True, **kwargs):
        self.name = name
        self.time = time
        self.verbose = verbose
        self.message = None
        self.message_printed = False

    def execute(self, satellite):
        raise NotImplementedError(
            f"{self.name} does not have a custom execute function!"
        )

    def print_message(self, message, satellite):
        if not self.message_printed:
            satellite.logger.info(message)
            self.message_printed = True

    def addFaultToSimulation(self, satellite, listIdx):
        self.uniqueFaultIdx = listIdx  # Index in the faultList array.
        satellite.simulator.createNewEvent(
            f"add{self.name}Fault",
            satellite.dynamics.dyn_rate,
            eventActive=True,
            conditionTime=self.time,
            actionList=[
                f"self.faultList[{self.uniqueFaultIdx}].execute({satellite._satellite_command})",
                f"self.faultList[{self.uniqueFaultIdx}].print({satellite._satellite_command})",
            ],
        )


class RwPowerFault(FaultObject):
    def __init__(self, name, time, reducedLimit, wheelIdx):
        super().__init__(name, time)
        self.reducedLimit = reducedLimit

        if isinstance(wheelIdx, float):
            # int needed around wheelIdx because np.random.choice doesn't return
            # a type int, and the index will not register in execute without it.
            self.wheelIdx = int(wheelIdx)
        elif isinstance(wheelIdx, int) or wheelIdx == "all":
            # option to trigger the fault in all wheels reflecting a larger power issue
            self.wheelIdx = wheelIdx
        else:
            raise ValueError(
                "Fault parameter 'wheelIdx' must either be a number corresponding to a reaction wheel or the string 'all'"
            )

    def execute(self, satellite):
        dynModels = satellite.dynamics
        if self.wheelIdx == 1:
            dynModels.rwFactory.rwList["RW1"].P_max = self.reducedLimit
        elif self.wheelIdx == 2:
            dynModels.rwFactory.rwList["RW2"].P_max = self.reducedLimit
        elif self.wheelIdx == 3:
            dynModels.rwFactory.rwList["RW3"].P_max = self.reducedLimit
        elif self.wheelIdx == 4:
            dynModels.rwFactory.rwList["RW4"].P_max = self.reducedLimit
        elif self.wheelIdx == "all":
            # option to trigger the fault in all wheels (not supported for all fault types)
            dynModels.rwFactory.rwList["RW1"].P_max = self.reducedLimit
            dynModels.rwFactory.rwList["RW2"].P_max = self.reducedLimit
            dynModels.rwFactory.rwList["RW3"].P_max = self.reducedLimit
            dynModels.rwFactory.rwList["RW4"].P_max = self.reducedLimit

    def print(self, satellite):
        if self.wheelIdx == "all":
            self.message = f"RW Power Fault: all RW's power limit reduced to {self.reducedLimit} Watts at {self.time * macros.NANO2MIN} minutes!"
        else:
            self.message = f"RW Power Fault: RW{self.wheelIdx}'s power limit reduced to {self.reducedLimit} Watts at {self.time * macros.NANO2MIN} minutes!"
        super().print_message(self.message, satellite)

Configure the Simulation Models

  • Dynamics model: FullFeaturedDynModel is used as the base class, and setup_reaction_wheel_dyn_effector is overridden to support four RWs. Two additional properties are added: the angle between the Sun and the solar panel, and the speed fraction of each RW.

[3]:
class CustomDynModel(dyn.FullFeaturedDynModel):
    @property
    def solar_angle_norm(self) -> float:
        sun_vec_N = (
            self.world.gravFactory.spiceObject.planetStateOutMsgs[self.world.sun_index]
            .read()
            .PositionVector
        )
        sun_vec_N_hat = sun_vec_N / np.linalg.norm(sun_vec_N)
        solar_panel_vec_B = np.array([0, 0, -1])
        mat = np.transpose(self.BN)
        solar_panel_vec_N = np.matmul(mat, solar_panel_vec_B)
        error_angle = np.arccos(np.dot(solar_panel_vec_N, sun_vec_N_hat))

        return error_angle / np.pi

    @property
    def wheel_speeds_frac(self):
        rw_speed = self.wheel_speeds
        return rw_speed[0:4] / (self.maxWheelSpeed * macros.rpm2radsec)

    @default_args(
        wheelSpeeds=lambda: np.random.uniform(-1500, 1500, 4),
        maxWheelSpeed=np.inf,
        u_max=0.200,
    )
    def setup_reaction_wheel_dyn_effector(
        self,
        wheelSpeeds: Iterable[float],
        maxWheelSpeed: float,
        u_max: float,
        priority: int = 997,
        **kwargs,
    ) -> None:
        """Set the RW state effector parameters.

        Args:
            wheelSpeeds: Initial speeds of each wheel [RPM]
            maxWheelSpeed: Failure speed for wheels [RPM]
            u_max: Torque producible by wheel [N*m]
            priority: Model priority.
            kwargs: Ignored
        """

        def balancedHR16Triad(
            useRandom=False, randomBounds=(-400, 400), wheelSpeeds=[500, 500, 500, 500]
        ):
            """Create a set of three HR16 reaction wheels.

            Args:
                useRandom: Use random values for wheel speeds.
                randomBounds: Bounds for random wheel speeds.
                wheelSpeeds: Fixed wheel speeds.

            Returns:
                tuple:
                    * **rwStateEffector**: Reaction wheel state effector instance.
                    * **rwFactory**: Factory containing defined reaction wheels.
                    * **wheelSpeeds**: Wheel speeds.
            """
            rwFactory = simIncludeRW.rwFactory()

            if useRandom:
                wheelSpeeds = np.random.uniform(randomBounds[0], randomBounds[1], 4)
            c = 3 ** (-0.5)
            rwFactory.create(
                "Honeywell_HR16",
                [1, 0, 0],
                maxMomentum=50.0,
                Omega=wheelSpeeds[0],
            )
            rwFactory.create(
                "Honeywell_HR16",
                [0, 1, 0],
                maxMomentum=50.0,
                Omega=wheelSpeeds[1],
            )
            rwFactory.create(
                "Honeywell_HR16",
                [0, 0, 1],
                maxMomentum=50.0,
                Omega=wheelSpeeds[2],
            )
            rwFactory.create(
                "Honeywell_HR16",
                [c, c, c],
                maxMomentum=50.0,
                Omega=wheelSpeeds[3],
            )

            rwStateEffector = reactionWheelStateEffector.ReactionWheelStateEffector()

            return rwStateEffector, rwFactory, wheelSpeeds

        self.maxWheelSpeed = maxWheelSpeed
        self.rwStateEffector, self.rwFactory, _ = balancedHR16Triad(
            useRandom=False,
            wheelSpeeds=wheelSpeeds,
        )
        for RW in self.rwFactory.rwList.values():
            RW.u_max = u_max
        self.rwStateEffector.ModelTag = "ReactionWheels"
        self.rwFactory.addToSpacecraft(
            self.scObject.ModelTag, self.rwStateEffector, self.scObject
        )
        self.simulator.AddModelToTask(
            self.task_name, self.rwStateEffector, ModelPriority=priority
        )

        self.Gs = np.array(
            [
                [1, 0, 0, 1 / np.sqrt(3)],  # RW1 and RW4 x-components
                [0, 1, 0, 1 / np.sqrt(3)],  # RW2 and RW4 y-components
                [0, 0, 1, 1 / np.sqrt(3)],  # RW3 and RW4 z-components
            ]
        )
  • Flight software model: A custom flight software model is defined to support four RWs. It is based on the SteeringImagerFSWModel, with the main modification being the addition of the rwNullSpace module. Due to the redundancy of having four RWs, there are infinitely many solutions for mapping the required body control torque to individual RW torques. To address this, once the control torque is computed, the RW null space is used to decelerate the wheels without applying additional torque to the spacecraft.

[4]:
class CustomSteeringImagerFSWModel(fsw.SteeringImagerFSWModel):
    def __init__(self, *args, **kwargs) -> None:
        """Convenience type that combines the imaging FSW model with MRP steering for four reaction wheels."""
        super().__init__(*args, **kwargs)

    def _set_config_msgs(self) -> None:
        super()._set_config_msgs()
        self._set_rw_constellation_msg()

    def _set_rw_constellation_msg(self) -> None:
        """Set the reaction wheel constellation message."""
        rwConstellationConfig = messaging.RWConstellationMsgPayload()
        rwConstellationConfig.numRW = self.dynamics.rwFactory.getNumOfDevices()
        rwConfigElementList = []
        for i in range(4):
            rwConfigElementMsg = messaging.RWConfigElementMsgPayload()
            rwConfigElementMsg.gsHat_B = self.dynamics.Gs[:, i]
            rwConfigElementMsg.Js = self.dynamics.rwFactory.rwList[f"RW{i + 1}"].Js
            rwConfigElementMsg.uMax = self.dynamics.rwFactory.rwList[f"RW{i + 1}"].u_max
            rwConfigElementList.append(rwConfigElementMsg)
        rwConstellationConfig.reactionWheels = rwConfigElementList
        self.rwConstellationConfigInMsg = messaging.RWConstellationMsg().write(
            rwConstellationConfig
        )

    def _set_gateway_msgs(self) -> None:
        """Create C-wrapped gateway messages."""
        self.attRefMsg = messaging.AttRefMsg_C()
        self.attGuidMsg = messaging.AttGuidMsg_C()

        self._zero_gateway_msgs()

        # connect gateway FSW effector command msgs with the dynamics
        self.dynamics.rwStateEffector.rwMotorCmdInMsg.subscribeTo(
            self.rwNullSpace.rwMotorTorqueOutMsg
        )
        self.dynamics.thrusterSet.cmdsInMsg.subscribeTo(
            self.thrDump.thrusterOnTimeOutMsg
        )

    class MRPControlTask(fsw.SteeringImagerFSWModel.MRPControlTask):
        def _create_module_data(self) -> None:
            super()._create_module_data()

            self.rwNullSpace = self.fsw.rwNullSpace = rwNullSpace.rwNullSpace()
            self.rwNullSpace.ModelTag = "rwNullSpace"

        def _setup_fsw_objects(self, **kwargs) -> None:
            super()._setup_fsw_objects(**kwargs)
            self.set_rw_null_space(**kwargs)

        @default_args(OmegaGain=0.3)
        def set_rw_null_space(
            self,
            OmegaGain: float,
            **kwargs,
        ) -> None:
            """Define the null space to slow down the wheels."""
            self.rwNullSpace.rwMotorTorqueInMsg.subscribeTo(
                self.rwMotorTorque.rwMotorTorqueOutMsg
            )
            self.rwNullSpace.rwSpeedsInMsg.subscribeTo(
                self.fsw.dynamics.rwStateEffector.rwSpeedOutMsg
            )
            self.rwNullSpace.rwConfigInMsg.subscribeTo(
                self.fsw.rwConstellationConfigInMsg
            )
            self.rwNullSpace.OmegaGain = OmegaGain
            self._add_model_to_task(self.rwNullSpace, priority=1193)

Configure the Satellite

  • Observations:

    • SatProperties: Body angular velocity, instrument pointing direction, body position, body velocity, battery charge (properties in flight software model or dynamics model). Also, customized dynamics property in CustomDynModel above: Angle between the sun and the solar panel and four RW speed fraction.

    • OpportunityProperties: Target’s priority, normalized location, and target angle (upcoming 32 targets).

    • Time: Simulation time.

    • Eclipse: Next eclipse start and end times.

  • Actions:

    • Desat: Manage momentum for the RWs for 60 seconds.

    • Charge: Enter a sun-pointing charging mode for 60 seconds.

    • Image: Image target from upcoming 32 targets

The fault is introduced by overriding the reset_post_sim_init function. The probability of the fault occurring can be specified using the fault_chance argument, and the time of occurrence can be set using the fault_time argument.

[5]:
class CustomSatComposed(sats.ImagingSatellite):
    observation_spec = [
        obs.SatProperties(
            dict(prop="omega_BP_P", norm=0.03),
            dict(prop="c_hat_P"),
            dict(prop="r_BN_P", norm=orbitalMotion.REQ_EARTH * 1e3),
            dict(prop="v_BN_P", norm=7616.5),
            dict(prop="battery_charge_fraction"),
            dict(prop="solar_angle_norm"),
            dict(prop="wheel_speeds_frac"),
        ),
        obs.OpportunityProperties(
            dict(prop="priority"),
            dict(prop="r_LP_P", norm=orbitalMotion.REQ_EARTH * 1e3),
            dict(prop="target_angle", norm=np.pi),
            type="target",
            n_ahead_observe=32,
        ),
        obs.Time(),
        obs.Eclipse(norm=5700),
    ]

    action_spec = [
        act.Desat(duration=60.0),
        act.Charge(duration=60.0),
        act.Image(n_ahead_image=32),
    ]

    # Modified the constructor to include the fault chance and list
    def __init__(self, *args, fault_chance=0, fault_time=0.0, **kwargs) -> None:
        super().__init__(*args, **kwargs)
        self.fault_chance = fault_chance
        self.fault_time = fault_time
        self.faultList = []  # List to store faults

    def reset_post_sim_init(self) -> None:
        super().reset_post_sim_init()

        if np.random.random() < self.fault_chance:
            powerFault = RwPowerFault(
                "rwPowerLimited", self.fault_time, reducedLimit=1.0, wheelIdx=1
            )
            self.faultList = [powerFault]
            self.simulator.faultList = self.faultList
            for i in range(len(self.faultList)):
                self.faultList[i].addFaultToSimulation(self, i)

    dyn_type = CustomDynModel
    fsw_type = CustomSteeringImagerFSWModel

Configure Satellite Pareameters

When instantiating a satellite, these parameters can be overriden with a constant or rerandomized every time the environment is reset using the sat_args dictionary.

[6]:
dataStorageCapacity = 20 * 8e6 * 100
batteryStorageCapacity = 80.0 * 3600 * 2
sat_args = CustomSatComposed.default_sat_args(
    oe=random_orbit,
    imageAttErrorRequirement=0.01,
    imageRateErrorRequirement=0.01,
    batteryStorageCapacity=batteryStorageCapacity,
    storedCharge_Init=lambda: np.random.uniform(0.4, 1.0) * batteryStorageCapacity,
    u_max=0.2,  # More realistic values than 1.0
    K1=0.5,  # Updated value to have smooth and more predictable control
    nHat_B=np.array([0, 0, -1]),
    imageTargetMinimumElevation=np.radians(45),
    rwBasePower=20,
    maxWheelSpeed=1500,
    storageInit=lambda: np.random.randint(
        0 * dataStorageCapacity,
        0.01 * dataStorageCapacity,
    ),
    wheelSpeeds=lambda: np.random.uniform(-900, 900, 4),
    disturbance_vector=lambda: random_unit_vector(),
)

# Make the satellites
satellites = []
satellites.append(
    CustomSatComposed(
        "EO",
        sat_args,
        fault_chance=1.0,
        fault_time=0.0,  # Fault occurs at 0.0 (nano seconds)
    )
)

Making and interacting the Environment

For this example, the single-agent SatelliteTasking environment is used. n addition to the configured satellite, the environment requires a scenario, which defines the context in which the satellite operates. In this case, the scenario uses UniformTargets, placing 1000 uniformly distributed targets across the Earth’s surface. The environment also takes a rewarder, which defines how data collected from the scenario is rewarded. Here, UniqueImageReward is used, which assigns rewards based on the sum of the priorities of uniquely imaged targets in each episode.

[7]:
env = SatelliteTasking(
    satellite=satellites,
    terminate_on_time_limit=True,
    scenario=scene.UniformTargets(n_targets=1000),
    rewarder=data.UniqueImageReward(),
    sim_rate=0.5,
    max_step_duration=300.0,
    time_limit=95 * 60 * 3,
    log_level="INFO",
    failure_penalty=0,
    # disable_env_checker=True, # For debugging
)

First, the environment is reset. A seed is provided to ensure reproducibility of the results; it can be removed to enable randomized testing.

[8]:
observation, info = env.reset(seed=1)
2026-07-18 03:51:21,446 gym                            INFO       Resetting environment with seed=1
2026-07-18 03:51:21,448 scene.targets                  INFO       Generating 1000 targets
/home/runner/work/bsk_rl/bsk_rl/src/bsk_rl/sim/dyn/base.py:330: BSKDeprecationWarning: Basilisk.utilities.unitTestSupport.np2EigenMatrix3d will be removed after 2027-06-23: Use simHelpers.np2EigenMatrix3d instead.
  self.scObject.hub.IHubPntBc_B = unitTestSupport.np2EigenMatrix3d(self.I_mat)
/home/runner/work/bsk_rl/bsk_rl/src/bsk_rl/sim/dyn/base.py:335: BSKDeprecationWarning: Basilisk.utilities.unitTestSupport.np2EigenVectorXd will be removed after 2027-06-23: Use simHelpers.np2EigenVectorXd instead.
  self.scObject.hub.r_CN_NInit = unitTestSupport.np2EigenVectorXd(rN)
/home/runner/work/bsk_rl/bsk_rl/src/bsk_rl/sim/dyn/base.py:336: BSKDeprecationWarning: Basilisk.utilities.unitTestSupport.np2EigenVectorXd will be removed after 2027-06-23: Use simHelpers.np2EigenVectorXd instead.
  self.scObject.hub.v_CN_NInit = unitTestSupport.np2EigenVectorXd(vN)
/home/runner/work/bsk_rl/bsk_rl/src/bsk_rl/sim/dyn/base.py:701: BSKDeprecationWarning: Basilisk.utilities.unitTestSupport.np2EigenVectorXd will be removed after 2027-06-23: Use simHelpers.np2EigenVectorXd instead.
  unitTestSupport.np2EigenVectorXd(nHat_B),
2026-07-18 03:51:21,499 sats.satellite.EO              INFO       <0.00> EO: Finding opportunity windows from 0.00 to 17400.00 seconds
2026-07-18 03:51:21,797 gym                            INFO       <0.00> Environment reset

The composed satellite action space returns a human-readable action map and each satellite has the same action space and similar observation space.

[9]:
print("Actions:", satellites[0].action_description)
print("States:", env.unwrapped.satellites[0].observation_description, "\n")

# Using the composed satellite features also provides a human-readable state:
for satellite in env.unwrapped.satellites:
    for k, v in satellite.observation_builder.obs_dict().items():
        print(f"{k}:  {v}")
Actions: ['action_desat', 'action_charge', 'action_image_0', 'action_image_1', 'action_image_2', 'action_image_3', 'action_image_4', 'action_image_5', 'action_image_6', 'action_image_7', 'action_image_8', 'action_image_9', 'action_image_10', 'action_image_11', 'action_image_12', 'action_image_13', 'action_image_14', 'action_image_15', 'action_image_16', 'action_image_17', 'action_image_18', 'action_image_19', 'action_image_20', 'action_image_21', 'action_image_22', 'action_image_23', 'action_image_24', 'action_image_25', 'action_image_26', 'action_image_27', 'action_image_28', 'action_image_29', 'action_image_30', 'action_image_31']
States: [np.str_('sat_props.omega_BP_P_normd[0]'), np.str_('sat_props.omega_BP_P_normd[1]'), np.str_('sat_props.omega_BP_P_normd[2]'), np.str_('sat_props.c_hat_P[0]'), np.str_('sat_props.c_hat_P[1]'), np.str_('sat_props.c_hat_P[2]'), np.str_('sat_props.r_BN_P_normd[0]'), np.str_('sat_props.r_BN_P_normd[1]'), np.str_('sat_props.r_BN_P_normd[2]'), np.str_('sat_props.v_BN_P_normd[0]'), np.str_('sat_props.v_BN_P_normd[1]'), np.str_('sat_props.v_BN_P_normd[2]'), np.str_('sat_props.battery_charge_fraction'), np.str_('sat_props.solar_angle_norm'), np.str_('sat_props.wheel_speeds_frac[0]'), np.str_('sat_props.wheel_speeds_frac[1]'), np.str_('sat_props.wheel_speeds_frac[2]'), np.str_('target.target_0.priority'), np.str_('target.target_0.r_LP_P_normd[0]'), np.str_('target.target_0.r_LP_P_normd[1]'), np.str_('target.target_0.r_LP_P_normd[2]'), np.str_('target.target_0.target_angle_normd'), np.str_('target.target_1.priority'), np.str_('target.target_1.r_LP_P_normd[0]'), np.str_('target.target_1.r_LP_P_normd[1]'), np.str_('target.target_1.r_LP_P_normd[2]'), np.str_('target.target_1.target_angle_normd'), np.str_('target.target_2.priority'), np.str_('target.target_2.r_LP_P_normd[0]'), np.str_('target.target_2.r_LP_P_normd[1]'), np.str_('target.target_2.r_LP_P_normd[2]'), np.str_('target.target_2.target_angle_normd'), np.str_('target.target_3.priority'), np.str_('target.target_3.r_LP_P_normd[0]'), np.str_('target.target_3.r_LP_P_normd[1]'), np.str_('target.target_3.r_LP_P_normd[2]'), np.str_('target.target_3.target_angle_normd'), np.str_('target.target_4.priority'), np.str_('target.target_4.r_LP_P_normd[0]'), np.str_('target.target_4.r_LP_P_normd[1]'), np.str_('target.target_4.r_LP_P_normd[2]'), np.str_('target.target_4.target_angle_normd'), np.str_('target.target_5.priority'), np.str_('target.target_5.r_LP_P_normd[0]'), np.str_('target.target_5.r_LP_P_normd[1]'), np.str_('target.target_5.r_LP_P_normd[2]'), np.str_('target.target_5.target_angle_normd'), np.str_('target.target_6.priority'), np.str_('target.target_6.r_LP_P_normd[0]'), np.str_('target.target_6.r_LP_P_normd[1]'), np.str_('target.target_6.r_LP_P_normd[2]'), np.str_('target.target_6.target_angle_normd'), np.str_('target.target_7.priority'), np.str_('target.target_7.r_LP_P_normd[0]'), np.str_('target.target_7.r_LP_P_normd[1]'), np.str_('target.target_7.r_LP_P_normd[2]'), np.str_('target.target_7.target_angle_normd'), np.str_('target.target_8.priority'), np.str_('target.target_8.r_LP_P_normd[0]'), np.str_('target.target_8.r_LP_P_normd[1]'), np.str_('target.target_8.r_LP_P_normd[2]'), np.str_('target.target_8.target_angle_normd'), np.str_('target.target_9.priority'), np.str_('target.target_9.r_LP_P_normd[0]'), np.str_('target.target_9.r_LP_P_normd[1]'), np.str_('target.target_9.r_LP_P_normd[2]'), np.str_('target.target_9.target_angle_normd'), np.str_('target.target_10.priority'), np.str_('target.target_10.r_LP_P_normd[0]'), np.str_('target.target_10.r_LP_P_normd[1]'), np.str_('target.target_10.r_LP_P_normd[2]'), np.str_('target.target_10.target_angle_normd'), np.str_('target.target_11.priority'), np.str_('target.target_11.r_LP_P_normd[0]'), np.str_('target.target_11.r_LP_P_normd[1]'), np.str_('target.target_11.r_LP_P_normd[2]'), np.str_('target.target_11.target_angle_normd'), np.str_('target.target_12.priority'), np.str_('target.target_12.r_LP_P_normd[0]'), np.str_('target.target_12.r_LP_P_normd[1]'), np.str_('target.target_12.r_LP_P_normd[2]'), np.str_('target.target_12.target_angle_normd'), np.str_('target.target_13.priority'), np.str_('target.target_13.r_LP_P_normd[0]'), np.str_('target.target_13.r_LP_P_normd[1]'), np.str_('target.target_13.r_LP_P_normd[2]'), np.str_('target.target_13.target_angle_normd'), np.str_('target.target_14.priority'), np.str_('target.target_14.r_LP_P_normd[0]'), np.str_('target.target_14.r_LP_P_normd[1]'), np.str_('target.target_14.r_LP_P_normd[2]'), np.str_('target.target_14.target_angle_normd'), np.str_('target.target_15.priority'), np.str_('target.target_15.r_LP_P_normd[0]'), np.str_('target.target_15.r_LP_P_normd[1]'), np.str_('target.target_15.r_LP_P_normd[2]'), np.str_('target.target_15.target_angle_normd'), np.str_('target.target_16.priority'), np.str_('target.target_16.r_LP_P_normd[0]'), np.str_('target.target_16.r_LP_P_normd[1]'), np.str_('target.target_16.r_LP_P_normd[2]'), np.str_('target.target_16.target_angle_normd'), np.str_('target.target_17.priority'), np.str_('target.target_17.r_LP_P_normd[0]'), np.str_('target.target_17.r_LP_P_normd[1]'), np.str_('target.target_17.r_LP_P_normd[2]'), np.str_('target.target_17.target_angle_normd'), np.str_('target.target_18.priority'), np.str_('target.target_18.r_LP_P_normd[0]'), np.str_('target.target_18.r_LP_P_normd[1]'), np.str_('target.target_18.r_LP_P_normd[2]'), np.str_('target.target_18.target_angle_normd'), np.str_('target.target_19.priority'), np.str_('target.target_19.r_LP_P_normd[0]'), np.str_('target.target_19.r_LP_P_normd[1]'), np.str_('target.target_19.r_LP_P_normd[2]'), np.str_('target.target_19.target_angle_normd'), np.str_('target.target_20.priority'), np.str_('target.target_20.r_LP_P_normd[0]'), np.str_('target.target_20.r_LP_P_normd[1]'), np.str_('target.target_20.r_LP_P_normd[2]'), np.str_('target.target_20.target_angle_normd'), np.str_('target.target_21.priority'), np.str_('target.target_21.r_LP_P_normd[0]'), np.str_('target.target_21.r_LP_P_normd[1]'), np.str_('target.target_21.r_LP_P_normd[2]'), np.str_('target.target_21.target_angle_normd'), np.str_('target.target_22.priority'), np.str_('target.target_22.r_LP_P_normd[0]'), np.str_('target.target_22.r_LP_P_normd[1]'), np.str_('target.target_22.r_LP_P_normd[2]'), np.str_('target.target_22.target_angle_normd'), np.str_('target.target_23.priority'), np.str_('target.target_23.r_LP_P_normd[0]'), np.str_('target.target_23.r_LP_P_normd[1]'), np.str_('target.target_23.r_LP_P_normd[2]'), np.str_('target.target_23.target_angle_normd'), np.str_('target.target_24.priority'), np.str_('target.target_24.r_LP_P_normd[0]'), np.str_('target.target_24.r_LP_P_normd[1]'), np.str_('target.target_24.r_LP_P_normd[2]'), np.str_('target.target_24.target_angle_normd'), np.str_('target.target_25.priority'), np.str_('target.target_25.r_LP_P_normd[0]'), np.str_('target.target_25.r_LP_P_normd[1]'), np.str_('target.target_25.r_LP_P_normd[2]'), np.str_('target.target_25.target_angle_normd'), np.str_('target.target_26.priority'), np.str_('target.target_26.r_LP_P_normd[0]'), np.str_('target.target_26.r_LP_P_normd[1]'), np.str_('target.target_26.r_LP_P_normd[2]'), np.str_('target.target_26.target_angle_normd'), np.str_('target.target_27.priority'), np.str_('target.target_27.r_LP_P_normd[0]'), np.str_('target.target_27.r_LP_P_normd[1]'), np.str_('target.target_27.r_LP_P_normd[2]'), np.str_('target.target_27.target_angle_normd'), np.str_('target.target_28.priority'), np.str_('target.target_28.r_LP_P_normd[0]'), np.str_('target.target_28.r_LP_P_normd[1]'), np.str_('target.target_28.r_LP_P_normd[2]'), np.str_('target.target_28.target_angle_normd'), np.str_('target.target_29.priority'), np.str_('target.target_29.r_LP_P_normd[0]'), np.str_('target.target_29.r_LP_P_normd[1]'), np.str_('target.target_29.r_LP_P_normd[2]'), np.str_('target.target_29.target_angle_normd'), np.str_('target.target_30.priority'), np.str_('target.target_30.r_LP_P_normd[0]'), np.str_('target.target_30.r_LP_P_normd[1]'), np.str_('target.target_30.r_LP_P_normd[2]'), np.str_('target.target_30.target_angle_normd'), np.str_('target.target_31.priority'), np.str_('target.target_31.r_LP_P_normd[0]'), np.str_('target.target_31.r_LP_P_normd[1]'), np.str_('target.target_31.r_LP_P_normd[2]'), np.str_('target.target_31.target_angle_normd'), np.str_('time'), np.str_('eclipse[0]'), np.str_('eclipse[1]')]

sat_props:  {'omega_BP_P_normd': array([0.00137284, 0.00080893, 0.00185074]), 'c_hat_P': array([-0.94095395, -0.07120216, -0.3309621 ]), 'r_BN_P_normd': array([-0.76023893, -0.76226973,  0.03873832]), 'v_BN_P_normd': array([-0.74001565,  0.72585949, -0.23976204]), 'battery_charge_fraction': 0.48805353449026784, 'solar_angle_norm': np.float64(0.3675725758375922), 'wheel_speeds_frac': array([ 0.2222634 , -0.3546573 ,  0.45374092])}
target:  {'target_0': {'priority': 0.6797657443023485, 'r_LP_P_normd': array([-0.72304393, -0.69048255,  0.02100749]), 'target_angle_normd': np.float64(0.6357597658378449)}, 'target_1': {'priority': 0.1011278274566988, 'r_LP_P_normd': array([-0.8839314 , -0.46366914, -0.06063175]), 'target_angle_normd': np.float64(0.3764086411837673)}, 'target_2': {'priority': 0.6931851990942818, 'r_LP_P_normd': array([-0.92043412, -0.36952122, -0.12749548]), 'target_angle_normd': np.float64(0.3723877146688926)}, 'target_3': {'priority': 0.17225514293500632, 'r_LP_P_normd': array([-0.92565997, -0.37833103, -0.00438879]), 'target_angle_normd': np.float64(0.38981813759316086)}, 'target_4': {'priority': 0.5711709172856598, 'r_LP_P_normd': array([-0.96343073, -0.26718398, -0.02034567]), 'target_angle_normd': np.float64(0.3943146022248573)}, 'target_5': {'priority': 0.39915339691165386, 'r_LP_P_normd': array([-0.9832796 , -0.17545716, -0.04874432]), 'target_angle_normd': np.float64(0.39937897834300234)}, 'target_6': {'priority': 0.3659991252731889, 'r_LP_P_normd': array([-0.99415125, -0.07715346, -0.07556872]), 'target_angle_normd': np.float64(0.4078843692651548)}, 'target_7': {'priority': 0.8196046614443331, 'r_LP_P_normd': array([-0.99765329, -0.01207943, -0.06739442]), 'target_angle_normd': np.float64(0.4168294389284707)}, 'target_8': {'priority': 0.31321450974410614, 'r_LP_P_normd': array([-0.97449116,  0.1725315 , -0.1435265 ]), 'target_angle_normd': np.float64(0.4358647819265422)}, 'target_9': {'priority': 0.9484757208286156, 'r_LP_P_normd': array([-0.96031054,  0.17441228, -0.21767872]), 'target_angle_normd': np.float64(0.433242760838707)}, 'target_10': {'priority': 0.48592850306846924, 'r_LP_P_normd': array([-0.96853779,  0.21402263, -0.12699944]), 'target_angle_normd': np.float64(0.4426489488945429)}, 'target_11': {'priority': 0.6184129633885858, 'r_LP_P_normd': array([-0.96210743,  0.21701823, -0.16508293]), 'target_angle_normd': np.float64(0.4411215055325246)}, 'target_12': {'priority': 0.17947175160982998, 'r_LP_P_normd': array([-0.94017117,  0.243405  , -0.23839502]), 'target_angle_normd': np.float64(0.4427323667761162)}, 'target_13': {'priority': 0.7384995398085523, 'r_LP_P_normd': array([-0.80487741,  0.52282763, -0.28075545]), 'target_angle_normd': np.float64(0.48648454206124414)}, 'target_14': {'priority': 0.27114812998614257, 'r_LP_P_normd': array([-0.76729423,  0.58576762, -0.26102845]), 'target_angle_normd': np.float64(0.4977256880591026)}, 'target_15': {'priority': 0.602211552115518, 'r_LP_P_normd': array([-0.69808315,  0.6848033 , -0.20910371]), 'target_angle_normd': np.float64(0.5172281968118192)}, 'target_16': {'priority': 0.379803286768697, 'r_LP_P_normd': array([-0.49501598,  0.82573585, -0.27040613]), 'target_angle_normd': np.float64(0.5507581988576493)}, 'target_17': {'priority': 0.4436831213331952, 'r_LP_P_normd': array([-0.45042693,  0.86931897, -0.20347018]), 'target_angle_normd': np.float64(0.5625207407345922)}, 'target_18': {'priority': 0.7048706468084478, 'r_LP_P_normd': array([-0.21420724,  0.9326702 , -0.29024395]), 'target_angle_normd': np.float64(0.59373704837557)}, 'target_19': {'priority': 0.9285111717464954, 'r_LP_P_normd': array([-0.19966509,  0.94633197, -0.25414496]), 'target_angle_normd': np.float64(0.5980174335717613)}, 'target_20': {'priority': 0.6283839193934228, 'r_LP_P_normd': array([ 0.04079828,  0.96062029, -0.27485298]), 'target_angle_normd': np.float64(0.6314125127394534)}, 'target_21': {'priority': 0.1929743249397491, 'r_LP_P_normd': array([ 0.0355612 ,  0.97627369, -0.21360027]), 'target_angle_normd': np.float64(0.6341742328673365)}, 'target_22': {'priority': 0.44341724161916973, 'r_LP_P_normd': array([ 0.11710105,  0.96569059, -0.23179522]), 'target_angle_normd': np.float64(0.6446733019141536)}, 'target_23': {'priority': 0.11836853522372437, 'r_LP_P_normd': array([ 0.34219224,  0.92570533, -0.16116486]), 'target_angle_normd': np.float64(0.6810789969475336)}, 'target_24': {'priority': 0.8270836989643272, 'r_LP_P_normd': array([ 0.37614852,  0.90638066, -0.19231846]), 'target_angle_normd': np.float64(0.6842502087329536)}, 'target_25': {'priority': 0.5185496026201819, 'r_LP_P_normd': array([ 0.38424706,  0.90105932, -0.20111263]), 'target_angle_normd': np.float64(0.6849377870859835)}, 'target_26': {'priority': 0.9675170836931263, 'r_LP_P_normd': array([ 0.38356319,  0.9111912 , -0.15036584]), 'target_angle_normd': np.float64(0.6878383017756565)}, 'target_27': {'priority': 0.9065897890064923, 'r_LP_P_normd': array([ 0.55753272,  0.82426831, -0.09868644]), 'target_angle_normd': np.float64(0.7179839245481688)}, 'target_28': {'priority': 0.9282669521531632, 'r_LP_P_normd': array([ 0.62887363,  0.76646723, -0.13056009]), 'target_angle_normd': np.float64(0.7278214487998897)}, 'target_29': {'priority': 0.07379201140065461, 'r_LP_P_normd': array([ 0.83349796,  0.55251892, -0.00199665]), 'target_angle_normd': np.float64(0.7770010755992804)}, 'target_30': {'priority': 0.010627938976362383, 'r_LP_P_normd': array([ 0.87933586,  0.46953401, -0.07941194]), 'target_angle_normd': np.float64(0.7821048162611637)}, 'target_31': {'priority': 0.13642904696262903, 'r_LP_P_normd': array([ 0.90564527,  0.41905752, -0.06478763]), 'target_angle_normd': np.float64(0.7904117166194159)}}
time:  0.0
eclipse:  [np.float64(0.7684210526315789), np.float64(0.14210526315789473)]

The simulation runs until either the battery is depleted, a RW exceeds its maximum speed (both considered failures), or a timeout occurs (which simply stops the simulation).

[10]:
total_reward = 0.0
while True:
    observation, reward, terminated, truncated, info = env.step(
        env.action_space.sample()
    )
    total_reward += reward
    if terminated or truncated:
        print("Episode complete.")
        break

print("Total reward:", total_reward)
2026-07-18 03:51:21,812 gym                            INFO       <0.00> === STARTING STEP ===
2026-07-18 03:51:21,813 sats.satellite.EO              INFO       <0.00> EO: target index 2 tasked
2026-07-18 03:51:21,814 sats.satellite.EO              INFO       <0.00> EO: Target(tgt-38) tasked for imaging
2026-07-18 03:51:21,815 sats.satellite.EO              INFO       <0.00> EO: Target(tgt-38) window enabled: 354.3 to 376.5
2026-07-18 03:51:21,815 sats.satellite.EO              INFO       <0.00> EO: setting timed terminal event at 376.5
2026-07-18 03:51:21,817 sats.satellite.EO              INFO       <0.00> EO: RW Power Fault: RW1's power limit reduced to 1.0 Watts at 0.0 minutes!
2026-07-18 03:51:21,818 sats.satellite.EO              INFO       <0.50> EO: imaged Target(tgt-38)
2026-07-18 03:51:21,818 data.base                      INFO       <0.50> Total reward: {'EO': 0.6931851990942818}
2026-07-18 03:51:21,819 comm.communication             INFO       <0.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,820 sats.satellite.EO              INFO       <0.50> EO: Satellite EO requires retasking
2026-07-18 03:51:21,825 gym                            INFO       <0.50> Step reward: 0.6931851990942818
2026-07-18 03:51:21,826 gym                            INFO       <0.50> === STARTING STEP ===
2026-07-18 03:51:21,827 sats.satellite.EO              INFO       <0.50> EO: target index 24 tasked
2026-07-18 03:51:21,827 sats.satellite.EO              INFO       <0.50> EO: Target(tgt-760) tasked for imaging
2026-07-18 03:51:21,828 sats.satellite.EO              INFO       <0.50> EO: Target(tgt-760) window enabled: 2273.6 to 2359.5
2026-07-18 03:51:21,829 sats.satellite.EO              INFO       <0.50> EO: setting timed terminal event at 2359.5
2026-07-18 03:51:21,831 sats.satellite.EO              INFO       <1.00> EO: imaged Target(tgt-760)
2026-07-18 03:51:21,832 data.base                      INFO       <1.00> Total reward: {'EO': 0.5185496026201819}
2026-07-18 03:51:21,832 comm.communication             INFO       <1.00> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,833 sats.satellite.EO              INFO       <1.00> EO: Satellite EO requires retasking
2026-07-18 03:51:21,838 gym                            INFO       <1.00> Step reward: 0.5185496026201819
2026-07-18 03:51:21,839 gym                            INFO       <1.00> === STARTING STEP ===
2026-07-18 03:51:21,839 sats.satellite.EO              INFO       <1.00> EO: target index 9 tasked
2026-07-18 03:51:21,840 sats.satellite.EO              INFO       <1.00> EO: Target(tgt-977) tasked for imaging
2026-07-18 03:51:21,841 sats.satellite.EO              INFO       <1.00> EO: Target(tgt-977) window enabled: 818.3 to 900.6
2026-07-18 03:51:21,842 sats.satellite.EO              INFO       <1.00> EO: setting timed terminal event at 900.6
2026-07-18 03:51:21,844 sats.satellite.EO              INFO       <1.50> EO: imaged Target(tgt-977)
2026-07-18 03:51:21,844 data.base                      INFO       <1.50> Total reward: {'EO': 0.48592850306846924}
2026-07-18 03:51:21,845 comm.communication             INFO       <1.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,845 sats.satellite.EO              INFO       <1.50> EO: Satellite EO requires retasking
2026-07-18 03:51:21,851 gym                            INFO       <1.50> Step reward: 0.48592850306846924
2026-07-18 03:51:21,852 gym                            INFO       <1.50> === STARTING STEP ===
2026-07-18 03:51:21,853 sats.satellite.EO              INFO       <1.50> EO: target index 9 tasked
2026-07-18 03:51:21,853 sats.satellite.EO              INFO       <1.50> EO: Target(tgt-336) tasked for imaging
2026-07-18 03:51:21,854 sats.satellite.EO              INFO       <1.50> EO: Target(tgt-336) window enabled: 810.7 to 925.8
2026-07-18 03:51:21,855 sats.satellite.EO              INFO       <1.50> EO: setting timed terminal event at 925.8
2026-07-18 03:51:21,857 sats.satellite.EO              INFO       <2.00> EO: imaged Target(tgt-336)
2026-07-18 03:51:21,857 data.base                      INFO       <2.00> Total reward: {'EO': 0.6184129633885858}
2026-07-18 03:51:21,858 comm.communication             INFO       <2.00> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,858 sats.satellite.EO              INFO       <2.00> EO: Satellite EO requires retasking
2026-07-18 03:51:21,864 gym                            INFO       <2.00> Step reward: 0.6184129633885858
2026-07-18 03:51:21,864 gym                            INFO       <2.00> === STARTING STEP ===
2026-07-18 03:51:21,865 sats.satellite.EO              INFO       <2.00> EO: target index 8 tasked
2026-07-18 03:51:21,866 sats.satellite.EO              INFO       <2.00> EO: Target(tgt-894) tasked for imaging
2026-07-18 03:51:21,867 sats.satellite.EO              INFO       <2.00> EO: Target(tgt-894) window enabled: 799.2 to 882.8
2026-07-18 03:51:21,867 sats.satellite.EO              INFO       <2.00> EO: setting timed terminal event at 882.8
2026-07-18 03:51:21,869 sats.satellite.EO              INFO       <2.50> EO: imaged Target(tgt-894)
2026-07-18 03:51:21,870 data.base                      INFO       <2.50> Total reward: {'EO': 0.9484757208286156}
2026-07-18 03:51:21,870 comm.communication             INFO       <2.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,871 sats.satellite.EO              INFO       <2.50> EO: Satellite EO requires retasking
2026-07-18 03:51:21,876 gym                            INFO       <2.50> Step reward: 0.9484757208286156
2026-07-18 03:51:21,877 gym                            INFO       <2.50> === STARTING STEP ===
2026-07-18 03:51:21,877 sats.satellite.EO              INFO       <2.50> EO: target index 31 tasked
2026-07-18 03:51:21,878 sats.satellite.EO              INFO       <2.50> EO: Target(tgt-841) tasked for imaging
2026-07-18 03:51:21,878 sats.satellite.EO              INFO       <2.50> EO: Target(tgt-841) window enabled: 3173.1 to 3281.6
2026-07-18 03:51:21,879 sats.satellite.EO              INFO       <2.50> EO: setting timed terminal event at 3281.6
2026-07-18 03:51:21,881 sats.satellite.EO              INFO       <3.00> EO: imaged Target(tgt-841)
2026-07-18 03:51:21,881 data.base                      INFO       <3.00> Total reward: {'EO': 0.3012131927347734}
2026-07-18 03:51:21,882 comm.communication             INFO       <3.00> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,882 sats.satellite.EO              INFO       <3.00> EO: Satellite EO requires retasking
2026-07-18 03:51:21,887 gym                            INFO       <3.00> Step reward: 0.3012131927347734
2026-07-18 03:51:21,888 gym                            INFO       <3.00> === STARTING STEP ===
2026-07-18 03:51:21,888 sats.satellite.EO              INFO       <3.00> EO: target index 15 tasked
2026-07-18 03:51:21,889 sats.satellite.EO              INFO       <3.00> EO: Target(tgt-239) tasked for imaging
2026-07-18 03:51:21,891 sats.satellite.EO              INFO       <3.00> EO: Target(tgt-239) window enabled: 1758.4 to 1865.8
2026-07-18 03:51:21,891 sats.satellite.EO              INFO       <3.00> EO: setting timed terminal event at 1865.8
2026-07-18 03:51:21,892 sats.satellite.EO              INFO       <3.50> EO: imaged Target(tgt-239)
2026-07-18 03:51:21,893 data.base                      INFO       <3.50> Total reward: {'EO': 0.9285111717464954}
2026-07-18 03:51:21,893 comm.communication             INFO       <3.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,894 sats.satellite.EO              INFO       <3.50> EO: Satellite EO requires retasking
2026-07-18 03:51:21,899 gym                            INFO       <3.50> Step reward: 0.9285111717464954
2026-07-18 03:51:21,900 gym                            INFO       <3.50> === STARTING STEP ===
2026-07-18 03:51:21,901 sats.satellite.EO              INFO       <3.50> EO: target index 9 tasked
2026-07-18 03:51:21,901 sats.satellite.EO              INFO       <3.50> EO: Target(tgt-804) tasked for imaging
2026-07-18 03:51:21,902 sats.satellite.EO              INFO       <3.50> EO: Target(tgt-804) window enabled: 1146.2 to 1196.2
2026-07-18 03:51:21,903 sats.satellite.EO              INFO       <3.50> EO: setting timed terminal event at 1196.2
2026-07-18 03:51:21,905 sats.satellite.EO              INFO       <4.00> EO: imaged Target(tgt-804)
2026-07-18 03:51:21,905 data.base                      INFO       <4.00> Total reward: {'EO': 0.7384995398085523}
2026-07-18 03:51:21,905 comm.communication             INFO       <4.00> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,906 sats.satellite.EO              INFO       <4.00> EO: Satellite EO requires retasking
2026-07-18 03:51:21,911 gym                            INFO       <4.00> Step reward: 0.7384995398085523
2026-07-18 03:51:21,912 gym                            INFO       <4.00> === STARTING STEP ===
2026-07-18 03:51:21,913 sats.satellite.EO              INFO       <4.00> EO: target index 13 tasked
2026-07-18 03:51:21,913 sats.satellite.EO              INFO       <4.00> EO: Target(tgt-364) tasked for imaging
2026-07-18 03:51:21,914 sats.satellite.EO              INFO       <4.00> EO: Target(tgt-364) window enabled: 1768.2 to 1822.8
2026-07-18 03:51:21,915 sats.satellite.EO              INFO       <4.00> EO: setting timed terminal event at 1822.8
2026-07-18 03:51:21,917 sats.satellite.EO              INFO       <4.50> EO: imaged Target(tgt-364)
2026-07-18 03:51:21,917 data.base                      INFO       <4.50> Total reward: {'EO': 0.7048706468084478}
2026-07-18 03:51:21,918 comm.communication             INFO       <4.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:21,919 sats.satellite.EO              INFO       <4.50> EO: Satellite EO requires retasking
2026-07-18 03:51:21,924 gym                            INFO       <4.50> Step reward: 0.7048706468084478
2026-07-18 03:51:21,924 gym                            INFO       <4.50> === STARTING STEP ===
2026-07-18 03:51:21,925 sats.satellite.EO              INFO       <4.50> EO: target index 26 tasked
2026-07-18 03:51:21,926 sats.satellite.EO              INFO       <4.50> EO: Target(tgt-524) tasked for imaging
2026-07-18 03:51:21,926 sats.satellite.EO              INFO       <4.50> EO: Target(tgt-524) window enabled: 3154.0 to 3193.7
2026-07-18 03:51:21,927 sats.satellite.EO              INFO       <4.50> EO: setting timed terminal event at 3193.7
2026-07-18 03:51:22,035 sim.simulator                  INFO       <304.50> Max step duration reached
2026-07-18 03:51:22,036 data.base                      INFO       <304.50> Total reward: {}
2026-07-18 03:51:22,036 comm.communication             INFO       <304.50> Optimizing data communication between all pairs of satellites
2026-07-18 03:51:22,042 sats.satellite.EO              WARNING    <304.50> EO: failed rw_speeds_valid check
2026-07-18 03:51:22,042 gym                            INFO       <304.50> Step reward: 0.0
2026-07-18 03:51:22,043 gym                            INFO       <304.50> Episode terminated: True
2026-07-18 03:51:22,043 gym                            INFO       <304.50> Episode truncated: False
Episode complete.
Total reward: 5.937646540098404