3
Different object types would require different motion
models. For instance, wheeled vehicles are controlled via
a set of steering tires and thus must be modeled as such.
A human, on the other hand, can change directions and
speeds very quickly and are erratic and indeterminate by
comparison, requiring a different motion model. The Path
Projection system uses the motion model associated with
the identified object type passed from the perception mod-
ule. Each motion model must accommodate all the rele-
vant contexts that are identified for that object. In a mine
environment, the number and type of objects are known
and limited (unlike the automotive world). Contexts and
associated motion models would need to be provided with
the equipment at purchase time, developed by third party
vendors, or created by the mine personnel.
Wheeled Vehicle Motion
Wheeled vehicles have the physics that motion in the direc-
tion of travel (velocity) is regulated by torque to the wheels,
and turning (angular velocity) is controlled by the angle of
the steering wheels. There are exceptions to this when lin-
ear and angular forces exceed what the surface will support
(wet roads, etc.). In general, linear and angular position
with three levels of derivative (velocity, acceleration, and
jerk) coupled with context is sufficient information to proj-
ect a few seconds into the future. An additional complexity
is the requirement that confidence be integral to the project
position and velocity as a function of time. Following is an
option for the math model that could be incorporated for
this task.
Model Structure
Using standard polynomial equations for position and rota-
tion, as well as modeling the way they interact with each
other, is a sound approach to creating elements for a matrix
solution system that will calculate projected state as well
as a covariance matrix that gives uncertainty for any data
point as a function of time. In reality, impact probability
is determined by proximity and variance at some point
in time, while severity of the interaction is a function of
velocity (speed and direction). MSA must complete that
projection for the “real” case (current truth) and also for
potentially thousands of alternate states being evaluated
by the Probability Processing Engine within the scan cycle
time of the perception system.
For polynomial displacement function, the basic model
would look like:
s s0 dt
ds s
2dt
1d
6dt
1dss
2
2
3 Dtd =+++n
And for the angular function:
dt
di d
2dt
1 1d
6dt 2
2 3
3 i i0 i i Dtd =+++n
where:
s =distance along the curve of travel
θ =angular position of the vehicle
t =time
Human Motion
Humans have inertia but are relatively indeterminant and
unconstrained in motion. Therefore, there is a significant
variance associated with any motion model represent-
ing humans in any environment in which they are free to
move. Human kinematics is vastly more complicated than
that of wheeled or tracked equipment. All this leads to
the need for a robustly comprehensive model and limited
confidence of future location. This, coupled with extreme
valuation of life and health, forces any Assured Autonomy
Safety Intervention System (AASIS) to automatically pro-
vide wide berth between humans and any operating auton-
omous equipment.
There has been much research into human motion
models (ref) that incorporate predictive behavior based
on limb segment motion for path projection at close range
(close enough for perception to discriminate limb segment
position) and more general motion at a distance (50 m).
These are expensive algorithms in terms of computing
resources, but also the most important because safety of
humans is of primary concern.
Stationary Equipment
Stationary equipment like conveyors, crushers, etc. present
significant hazards to operators because they have moving
parts, elevated surfaces, electricity, hot surfaces, and other
characteristics that can be hazardous. Each hazard has an
associated mechanism of injury and a field of danger that can
be modeled with affiliated context. This field is not binary
(a hard line within which danger exists), rather it typically
possesses a statistical distribution of danger that is often
context dependent. An example of this would be an open
electrical panel. It is only dangerous when it is energized. In
this paradigm, an AASIS equipment monitor would typi-
cally be modeling human movement within context driven
fields of danger that can trigger intervention responses like
sensory warning (auditory, visual, tactile, etc.), change of
state (slow or stop motion, lock a gate, remove power, etc.),
or any other action that the machine can control that would
reduce the project risk of a human’s actions.
Different object types would require different motion
models. For instance, wheeled vehicles are controlled via
a set of steering tires and thus must be modeled as such.
A human, on the other hand, can change directions and
speeds very quickly and are erratic and indeterminate by
comparison, requiring a different motion model. The Path
Projection system uses the motion model associated with
the identified object type passed from the perception mod-
ule. Each motion model must accommodate all the rele-
vant contexts that are identified for that object. In a mine
environment, the number and type of objects are known
and limited (unlike the automotive world). Contexts and
associated motion models would need to be provided with
the equipment at purchase time, developed by third party
vendors, or created by the mine personnel.
Wheeled Vehicle Motion
Wheeled vehicles have the physics that motion in the direc-
tion of travel (velocity) is regulated by torque to the wheels,
and turning (angular velocity) is controlled by the angle of
the steering wheels. There are exceptions to this when lin-
ear and angular forces exceed what the surface will support
(wet roads, etc.). In general, linear and angular position
with three levels of derivative (velocity, acceleration, and
jerk) coupled with context is sufficient information to proj-
ect a few seconds into the future. An additional complexity
is the requirement that confidence be integral to the project
position and velocity as a function of time. Following is an
option for the math model that could be incorporated for
this task.
Model Structure
Using standard polynomial equations for position and rota-
tion, as well as modeling the way they interact with each
other, is a sound approach to creating elements for a matrix
solution system that will calculate projected state as well
as a covariance matrix that gives uncertainty for any data
point as a function of time. In reality, impact probability
is determined by proximity and variance at some point
in time, while severity of the interaction is a function of
velocity (speed and direction). MSA must complete that
projection for the “real” case (current truth) and also for
potentially thousands of alternate states being evaluated
by the Probability Processing Engine within the scan cycle
time of the perception system.
For polynomial displacement function, the basic model
would look like:
s s0 dt
ds s
2dt
1d
6dt
1dss
2
2
3 Dtd =+++n
And for the angular function:
dt
di d
2dt
1 1d
6dt 2
2 3
3 i i0 i i Dtd =+++n
where:
s =distance along the curve of travel
θ =angular position of the vehicle
t =time
Human Motion
Humans have inertia but are relatively indeterminant and
unconstrained in motion. Therefore, there is a significant
variance associated with any motion model represent-
ing humans in any environment in which they are free to
move. Human kinematics is vastly more complicated than
that of wheeled or tracked equipment. All this leads to
the need for a robustly comprehensive model and limited
confidence of future location. This, coupled with extreme
valuation of life and health, forces any Assured Autonomy
Safety Intervention System (AASIS) to automatically pro-
vide wide berth between humans and any operating auton-
omous equipment.
There has been much research into human motion
models (ref) that incorporate predictive behavior based
on limb segment motion for path projection at close range
(close enough for perception to discriminate limb segment
position) and more general motion at a distance (50 m).
These are expensive algorithms in terms of computing
resources, but also the most important because safety of
humans is of primary concern.
Stationary Equipment
Stationary equipment like conveyors, crushers, etc. present
significant hazards to operators because they have moving
parts, elevated surfaces, electricity, hot surfaces, and other
characteristics that can be hazardous. Each hazard has an
associated mechanism of injury and a field of danger that can
be modeled with affiliated context. This field is not binary
(a hard line within which danger exists), rather it typically
possesses a statistical distribution of danger that is often
context dependent. An example of this would be an open
electrical panel. It is only dangerous when it is energized. In
this paradigm, an AASIS equipment monitor would typi-
cally be modeling human movement within context driven
fields of danger that can trigger intervention responses like
sensory warning (auditory, visual, tactile, etc.), change of
state (slow or stop motion, lock a gate, remove power, etc.),
or any other action that the machine can control that would
reduce the project risk of a human’s actions.