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«The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213 May 13, 2005 Submitted in partial fulfillment of the requirements for the ...»

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Line-of-Sight Maps - Line-of-sight (LOS) maps encode the elevation angle of a source object above the local ground plane as defined by the slope map (see Figure 4-3 for an example). They also map shadowed locations, where the source is below the ground plane or occluded by other terrain features. LOS maps currently represent incident sunlight for the purpose of modeling solar energy, lighting and shadowing. However, they could also represent line-ofsight to orbiting spacecraft or visibility to fixed points elsewhere on the terrain surface. A ray tracing algorithm


projects from the source position (e.g. a Solar System body) onto the terrain model. Sequences of LOS maps, at regular time intervals, represent time-varying visibility.

Solar Flux - The incident energy per unit area is modeled by the peak flux (as experienced under perpendicular incidence) multiplied by the sine of the sun elevation angle to capture foreshortening effects. Atmospheric attenuation must be captured in the peak flux value - the World Model currently assumes no variation in flux with angle from zenith. We currently ignore all other effects. This model is used principally for the computation of available solar power, but might also be used to compute the sun’s thermal influence on vehicle components.

4.2.2 Rover Model The path planner must be able to predict the effects of activities undertaken under different environmental conditions.

The basic unit of the Rover Model is the rover component model. Components model mission-relevant units or capabilities of the rover, and include parameters relevant to operational constraints on the rover. Each component in the Rover Model can be activated or de-activated based on the activity being performed. Active components can be set to a continuous range of activity level, defined by a duty cycle. The Rover Model aggregates components and utilizes the World Model to predict how activated components affect the rover internal and external state.

As with the World Model, the Rover Model must be set to a particular state which in turn defines the behavior of rover components. In this thesis, since the emphasis of TEMPEST has been on path planning that enables energy management, the Rover Model uses only battery energy state. The Rover Model predicts power load as a summation of the powers from each activated component, scaled by their duty cycles. However, one could envision modeling other resources similarly, for example component wear, component thermal state, or available computer memory. Science data might be analogous to energy, and onboard memory the equivalent of a battery - science data collection and communications with Earth would then be the activity equivalents of battery charging and discharging, respectively. The

following are a few examples of rover components that are possible in the Rover Model:

Locomotor - A component that models the speed and power of a vehicle as a function of terrain, and determines whether or not terrain is traversable. One simplified instantiation of the model is parameterized on vehicle mass, drivetrain efficiency, and effective coefficient of friction. Other, more sophisticated models might incorporate models of bulldozing resistance, rolling resistance and slippage.

Battery - A component that models energy storage capacity. A basic model might simply encode minimum and maximum bounds on charge. More sophisticated models could incorporate charge and discharge rate limits, transmission losses, and might model individual cells in the battery.


Solar Array - The solar array is a pointed component model. A simple model encodes the array normal vector with respect to the vehicle frame, the array area, and the solar cell efficiency. More complicated models might incorporate models of individual cells, the strings of cells, and degradation effects due to dust collection or radiation.

Power Load Component - A generic component type, the power load component describes a fixed power load (positive) or power source (negative) in the system. The component models steady loads for onboard electronics (positive loads) or the power coming from a radioisotope thermoelectric generator (RTG - a negative load).

Field Of View Component - A generic pointed component type that models the field of view of sensing devices on the vehicle. Used in defining geometric constraints, this component might define cameras, sun sensors or communications antennas, and is not required to specify the component power.

To date, the emphasis of TEMPEST planning has been on path planning that enables energy management. Therefore, most rover components predict power load as a summation of the powers from each active component, scaled by their duty cycles. One might envision modeling other resources similarly. Components might also model thermal energy or component wear as a function of World Model conditions.

4.2.3 Constraint Set Constraints in TEMPEST encode the set of world and rover state values under which an action is illegal. They can represent either physically impossible conditions, or conditions that are undesirable operationally. The Constraint Set aggregates a number of individual constraints, each of which can be activated or de-activated for selective application to different actions.

To test for constraint satisfaction or violation under certain conditions, the Constraint Set sets the World Model and Rover Model states to the test condition, then checks each activated constraint for a violation. The individual constraints access the World Model and Rover Model local state parameter values to compute Boolean constraint violation functions. Because they depend only on current world and rover state, Constraint Set constraints are local as

opposed to global. The following examples give a flavor for the kinds of constraints that are possible:

Position - Actions might either be restricted to or restricted from operating within a particular area on a map. The position constraint enables a user to specify a set of positions, and whether the positions define a legal or illegal region. This constraint is useful for defining hazardous regions not otherwise modeled in the World Model, or perhaps scientifically interesting regions within which a particular set of measurements is useful.


Maximum Slope - Slopes present a hazard to rover driving. Driving on a steep slope can risk vehicle tipover. Even if tipover is not an issue, steep slopes may be impossible to climb due to limited traction. In the simplest model, a user can select a maximum slope that is legal to operate on. This model calls exclusively on the World Model.

Direct Line of Sight - Line-of-sight (LOS) geometry is important for a number of applications, including solar power collection, communications and remote sensing. A source is within LOS of the vehicle if a ray from the source to the vehicle does not intersect the terrain surface. The LOS constraint allows a user to specify a source object in the World Model with which LOS geometry must be evaluated during search. The constraint can be defined either to succeed or fail if LOS conditions exist. A user might define a “shadowed” constraint to define the illegal conditions for solar charging, or a “sunlit” constraint to define illegal conditions for a thermal cooling action. Note that a “shadowed” constraint does not distinguish between simple terrain occlusion and below-horizon conditions. Similar constraints could be generated for other sources (e.g. “out of view of Earth”, “in view of Mars Odyssey”, or “out of view of alluvial fan X”).

Elevation Angle - The elevation angle constraint limits the geometry of a Solar System object with respect to the local horizontal plane. A user must define the source object, the threshold elevation angle and whether the illegal range is above or below the threshold elevation. The primary use of the elevation angle constraint is to define the elevation angle threshold for “daytime” or “nighttime” conditions.

Field of View - Sensor geometry can often be defined in terms of a boresight vector and its field of view (FOV), an angle about the boresight defining its cone of sensitivity. The user defines an FOV constraint by selecting an FOV component from the Rover Model and a source object from the World Model (for example the sun), and designates whether the constraint is violated when the object falls within or outside the FOV. One might define the range of sunboresight angles for which a sun sensor returns accurate vehicle heading estimates, or the spacecraft-boresight angle range when communication are possible to an orbiting relay satellite.

Time Bounds - A mission might require or disallow actions to fall within a fixed time range. This constraint permits actions to be constrained within or outside a time bounds.

Battery Charge - This constraint specifies the legal range of battery state-of-charge. To specify this constraint, a user associates the constraint with a specific battery model defined in the Rover Model. Hence the range is defined by the Rover Model. A particularly power-hungry activity might require a high state of charge. Alternatively, stopping to charge a battery using solar energy might only be justified when the state of charge is below a certain threshold.


Multiple constraints can be applied to a single action to dictate more complicated constraint conditions. For example, one could define a “Prevent Sun Blinding” constraint, to specify the conditions under which a camera is blinded by the sun. It might combine the “Direct Line of Sight” and camera “FOV” constraints, since the FOV constraint by itself would ignore whether the sun is actually visible or occluded from view. A constraint to identify times near sunrise and sunset might combine two sun elevation constraints, for example “Sun Above the Horizon” and “Sun Below 10 Degrees Elevation”.

4.2.4 Action Set The Action Set aggregates the actions that are most relevant to the planning problem. The central theme of path planning is to plan for motion through an environment - therefore motion actions are required in all domains. Other action types are optional. In domains where resource management is important, the Action Set might include actions for resource collection (e.g. battery charging) and must represent salient resource consumption activities. If mission goal-related actions (e.g. science data collection) consume significant time or resources, or if constraints imposed on them might affect the route or schedule, then they must also be included.

Table 4-1 lists the data required to define a TEMPEST action. The World Model and Rover Model play a substantial role in the behavior of the action. Given the target change in state (Line 1), the active rover components (Line 2) determine the change in other state variables. For instance, if a Drive action targets a change in X and Y position, the rover components determine, through speed and power equations, the resulting change in time and battery energy.

Through Line 4, constraints can modify the behavior of the Rover Model by allowing actions in some states and preventing them in others. Line 3 is a condition that allows TEMPEST to remove vehicle heading from the search space.

In most cases the optimal rover orientation is either a direct function of the target change in state, or more a function of local state than of global path state history.

–  –  –

1. A target change in state. Mobile actions specify a target change in position. Stationary actions result in zero net change in position, and so specify changes in other state parameters.

2. A list of active Rover Model components and their duty cycles. The components must enable the target state change, and must uniquely determine the resulting change in all other state parameters.

3. A function θ = f ( s, a ) that uniquely determines the vehicle orientation as a function of state.

4. A list of active Constraint Set members to be actively enforced.

An important limitation is that TEMPEST only solves for plans that are sequences of fully-ordered actions. This research has not actively sought a scalable means of representing parallel actions. Currently, parallel actions can be


approximated by combining the behaviors of each action into a single action model, but representing all possible action combinations would result in an exponential growth of the action space.

The following examples of TEMPEST actions illustrate how the conditions in Table 4-1are met:

Drive - An action to enable vehicle mobility in a plan. The data required to define a drive action are listed in Table 4The simplest drive actions enable motion to each of the eight neighbors in an eight-connected grid map. Each cell destination defines a separate action. The vehicle orientation is a direct consequence of the position target - the vehicle must face in the driving direction to achieve the target cell1. Vehicle speed is defined by local terrain parameters and rover parameters.

–  –  –

One or more rover components must yield the change in time and resource state variables for the target position change. Specifically, the component must specify the vehicle speed and power given the state (e.g. as a function of local terrain, available solar power and sunlight, vehicle mass, etc.). Fixing the speed is not a substantial limitation of the model. Current planetary rovers are typically designed to drive at a single speed. Control strategies may command lower speeds when following sharper turns or when in hazardous terrain. Though neither turning radii nor local obstacles are explicitly represented at the low resolution of global planning, their long-term effects can be captured in an average speed model. If a single speed does not adequately model the vehicle’s motion, one can define multiple drive actions that have the same position change but utilize locomotor components with different speeds.

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