Trajectory Generation for Effective Sensing


Intelligence, surveillance, and reconaissance (ISR) missions represent a consistent theme among both existing and proposed applications for unmanned systems. Emerging sensor and control technologies will enable future systems to play an increasingly prevalent role in both civil and military applications. For example, unmanned air vehicles (UAVs) might be used in the future for tasks such as traffic monitoring, as depicted in Figure 2. Automation of these sensing tasks can be expected to yield a number of significant benefits despite posing a number of significant technical challenges.

Predator Traffic Monitoring MAV
Figure 1: The Predator Drone Figure 2: UAV Monitoring Traffic

Participation of current unmanned sensing systems, such as the Predator drone (Figure 1), is often passive in nature and occurs from a distant vantage point that is significantly removed from the sensing objective. Proposed multi-role mission scenarios might require future systems to autonomously search for, detect, classify, and track targets through environments of varying scale. Missions that involve environment scale approaching that of the characteristic dimensions of the vehicle dynamics introduce unique challenges. Specifically, aggressive vehicle trajectories through such environments result in significant coupling between the tasks of vehicle navigation and sensor-pointing. Variations in data quality that result from changes in aspect and sensing geometry canot be neglected. Further, realistic dynamic constraints must be considered in order to ensure precision trajectory tracking. This requirement is imposed by the small allowable error margins resulting from trajectories that weave through closely-spaced obstacles.

This project aims to address some of the discussed challenges associated with sensor autonomy. Specifically, a trajectory planning approach is developed for dynamically-constrained vehicles that carry a remote sensor. The inherent coupling between vehicle motion and the quality of sensed data over the sensor field of view (FOV) is explicitly considered. A metric relating "sensor quality" is developed and used to evaluate performance of the trajectory planner.

Modeling and Planning

A motion model is adopted that allows dynamic motion constraints to be considered explicitly in the motion plan. The vehicle dynamics are often represented by a set of highly coupled, nonlinear differential equations. An alternative approach involves the use of hybrid modeling strategies. Specifically, the proposed strategy employs a finite set of dynamically-consistent motion primitives to quantize the continuous vehicle model.

Vehicle motions are classified as either steady trim trajectories or unsteady finite-duration maneuvers. Further, the allowable switching behavior is characterized amongst a finite set of motions falling into these classes. The set of selected trim motions and the interconnecting maneuvers are encoded as a state-machine. Therefore, the complex continuous dynamics are replaced with a much simpler finite-state hybrid system. Hence, once motion primitives are computed and switching behavior is characterized in this framework, a relatively few variables describe a large reachable set of states.

Randomized motion planning methods have recently emerged as a powerful tool for complex planning problems. These methods are particularly useful for addressing planning problems that involve dynamics. The approach involves growing a tree consisting of trajectory segments to explore the action space, or reachable set, of the system. This tree is expanded in directions that efficiently cover the action space and favorably affect the value of a specified performance metric. In this fashion, a large number of efficiently generated, performance-guided candidate solutions can be evaluated in lieu of finding a single, computationally-intensive optimal solution. Moreover, randomized planning methods are well-suited to the hybrid modeling framework discussed previously, as solution-tree branches will simply consist of strings of concatenated motion primitives.

Randomized Planner

Sensor Quality

A key element of the required work is the concept of "sensor quality" as a measure of information gain. Information theory provides a solid, quantitative approach to assess the statistical properties of sensed data; however, these concepts often fail to account for realistic modeling of the sensing process. The definition of "sensed" is often binary in nature with respect to inclusion within the sensor FOV. In reality, geometric factors such as range and relative aspect, along with characteristics specific to the given sensor, define continuously-varying sensor quality within the FOV.

The definition of a sensor quality metric varies among different sensor modalities due to specific physical characteristics. This project considers a class of line-of-sight (LOS) sensors and the associated geometric quality-affecting factors in an attempt to generalize the concept of sensor quality. This class of sensors includes cameras, radar, sonar, and laser rangers, among others. The geometric characteristics of such sensors are depicted in Figure 3. Data quality within the sensor footprint is decomposed into elements associated with the range, r, incidence angle, &sigma, and FOV angle, &epsilon . Additional factors such as coverage area and the flow rate of data through the FOV are under consideration as well.

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Figure 3: Sensor Geometry

The quality function, Q, is defined as the composition of "efficiency functions" that depend on the geometric factors described by Figure 3. The proposed general shapes of the efficiency functions, &fnofr , &fnof&sigma, and &fnof&epsilon , are shown by Figure 4.

Q = &fnofr&fnof&sigma&fnof&epsilon

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Figure 4: Quality "Efficiency Functions"

Several snapshots are shown below of a simulated trajectory for a UAV carrying a forward-pointing LOS sensor (such as a camera) that is fixed to the aircraft body at an elevation angle of -45° . The geometric factors affecting sensor quality are seen to be a function of the position and orientation of both the sensor and the target surface. Vehicle attitude changes are seen to affect the size and shape of the sensor footprint. The associated variations in range and incidence obviously present a tradeoff between coverage area and sensor quality. Application of information-theoretic techniques as planning criteria must account for this behavior, as the quality of information gained must be considered in addition to quantity.

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Sensor quality can be incorporated into a cost function to use as a performance metric for motion planning purposes. For example, Figure 5 shows the maximum quality at sensed points in the environment over a prespecified trajectory. Such information can be used to plan motions that ensure high quality data for targets and desired locations. Additional elements such as time, control energy, and threat risk can also be incorporated into such performance criteria.

Randomized Planner
Figure 5: Aggregate Sensor Quality