GravityBiasedJointStopScenario

Robotics scenarios · Implementation: mlsysim/engine/scenario_definitions/robotics/control.py.

Construct this scenario with keyword inputs. The fields below show the types and defaults declared by this class.

One loaded arm joint at joint_speed braking with machine’s peak torque while gravity holds bias_fraction of that peak along (descending) or against (ascending) the motion.

Braking deceleration is net torque over inertia; the joint stops in w^2 / (2 alpha) and the tool at lever travels that angle times the lever. The kinetic barrier h = theta - w^2 / (2 alpha_net) (descending) bounds the next torque by tau <= -tau_bias + I alpha_net (gamma h / w - 1); its negative is the braking torque the barrier demands at a tool clearance. With site, the protective separation distance prices a person at the site’s approach speed over the site’s pre-brake delay plus the descending joint stop, the tool’s reaction travel, and the tool’s stop.

Notes

Equation: tool_stop_descending is the worked quantity; each property below states its equation and units.

Assumptions: Single-joint inertia, lever arm, gravity bias, and available braking torque stay constant.

Excludes: Multibody dynamics, torque slew, brake onset variation, and safety certification.

References

Derivation: The equations below follow the stated counts, geometric relations, or accounting definitions; scenario inputs are supplied assumptions or observations, not fitted predictions.

Examples

Execute the registered worked inputs; this is a modeled calculation.

>>> from mlsysim import Scenarios
>>> case = Scenarios.LoadedArmJointGravityStop
>>> value = case.tool_stop_descending
>>> print(f"{value:.3f~P}")
79.448 mm

Attributes

Name	Description
alpha_ascending	Ascending constant angular deceleration in inverse seconds squared.
alpha_descending	Descending constant angular deceleration in inverse seconds squared.
alpha_free	Unbiased constant angular deceleration in inverse seconds squared.
barrier_clearances
barrier_demands	Required braking torques in N m for every listed clearance.
barrier_gain
bias	Constant gravitational bias torque in N m, specified fraction of peak torque.
bias_fraction
inertia
joint_speed
lever
machine
overrun	Extra descending stop travel in mm compared with the unbiased stop.
separation_person	Human approach travel in mm during reaction and descending joint stopping.
separation_person_share	Dimensionless human-travel share of the separation total.
separation_reaction	Tool reaction travel in mm before braking begins.
separation_total	Total human, reaction, and stopping travel in mm before additional margins.
site
stop_time_descending	Descending joint stopping duration in ms.
tcp_speed	Tool tangential speed in m/s at the specified lever arm.
tool_stop_ascending	Tool stopping arc length in mm when gravity assists braking.
tool_stop_descending	Tool stopping arc length in mm when gravity opposes braking.
tool_stop_free	Tool stopping arc length in mm without gravity bias.
torque_ascending	Net ascending braking torque in N m after adding gravity assistance.
torque_descending	Net descending braking torque in N m after subtracting gravity bias.
torque_limit	Configured joint peak torque in N m.

Methods

Name	Description
barrier_margin	Kinetic barrier margin in radians at the supplied tool clearance.
barrier_torque_demand	Required braking torque in N m from the stated kinetic-barrier inequality.
stop_angle	Joint stopping angle in radians at supplied positive angular deceleration.
tool_stop	Tool stopping arc length in mm at supplied angular deceleration.

barrier_margin

engine.scenario_types.GravityBiasedJointStopScenario.barrier_margin(clearance)

Kinetic barrier margin in radians at the supplied tool clearance.

Kinetic barrier h = theta - w^2 / (2 alpha_net) at a tool clearance (radians).

Equation: return (clearance / self.lever).to(’’).magnitude - self.stop_angle(self.alpha_descending)

barrier_torque_demand

engine.scenario_types.GravityBiasedJointStopScenario.barrier_torque_demand(
    clearance,
)

Required braking torque in N m from the stated kinetic-barrier inequality.

Braking torque the barrier demands at a tool clearance (the bound’s negative).

Equation: h = self.barrier_margin(clearance) bound = (-self.bias + self.inertia * self.alpha_descending * (self.barrier_gain * h / self.joint_speed - 1)).to(‘N*m’) return (-bound).to(‘N*m’)

stop_angle

engine.scenario_types.GravityBiasedJointStopScenario.stop_angle(alpha)

Joint stopping angle in radians at supplied positive angular deceleration.

Joint stop angle in radians at deceleration alpha.

Equation: return (self.joint_speed ** 2 / (2 * alpha)).to(’’).magnitude

tool_stop

engine.scenario_types.GravityBiasedJointStopScenario.tool_stop(alpha)

Tool stopping arc length in mm at supplied angular deceleration.

Equation: return (self.lever * self.stop_angle(alpha)).to(‘mm’)