Brian J. Goode

A graph theoretical approach toward a switched feedback controller for pursuit-evasion scenarios

This research introduces a novel method for constructing a switched feedback control system to be used for an autonomous agent. The state space is partitioned into sets of states where a specific control is applied. Each partition is represented by nodes of a digraph where the success of the control in traversing the partitions is represented by a connecting edge. Using the concept of capture sets in the field of differential games, it is shown that a set of states included in a particular partition is capable of reaching the target set if the eigenvalues of the adjacency matrix representing the digraph are all zero and none of the partitions are invariant. The advantage of this method is that it is possible to assign finite horizon controls to each partition that are easier to calculate than infinite horizon methods, but still maintain the infinite horizon guarantee of reaching the target. An example is given to illustrate the implementation of the proposed controller.

A Differential Game Theoretic Approach for Two-Agent Collision Avoidance with Travel Limitations

This work presents a collision avoidance control strategy that solves the Hamilton-Jacobi-Isaacs (HJI) equation for an agent to quickly take action assuming a worst-case scenario. By doing so, the agent can develop a control strategy that is robust to the strategies of other agents with whom collision is possible. Consequently, if the governing dynamics of the agent are sufficient, then a collision can be avoided. We build on the idea of finding control solutions by using a differential game theoretic approach (Mettenheim and Breitner, 2009). This is beneficial because the opposing agent’s strategy is incorporated into the control by assuming it plays the worst-case actions. The approach in this work solves the zero-sum aspects of the control on-line using a fast solution method that operates over partitions in the state space (Goode et al., ASME J Dyn Syst Meas Control, 2011). We form the solution to the Homicidal Chauffeur game which is used to provide the control for an evader attempting to avoid a pursuer, an agent that deviates from its normal path and into that of the evader. Furthermore, the evader is constrained to remain within defined boundaries of its assigned travel area, such as a road lane, water channel, etc. The control strategy consists of three parts: (1) a zero-sum approximation of collision avoidance, (2) high-level path planning, and (3) low-level vehicle control. Each component is explained, and an example is given using a real robotic vehicle control system. Here, we show how the control can be implemented using a simple processor located on a vehicle that seeks to avoid a collision with another oncoming vehicle, making a left turn.

Pursuit-evasion with acoustic sensing using one step nash equilibria

In this paper, we derive a non-zero-sum multiplayer game that models pursuit-evasion tactics in an acoustic field. Specifically, the Pursuer uses acoustic sensing to determine the location of the Evader. However, this sensing ability is corrupted by noise generated from the motion of both the Pursuer and Evader. It is argued that the dominant mechanism of sensory degrading noise from the Pursuer is a function of speed, while the noise from the Evader is a function of acceleration and speed. Depending on the set of parameters characterizing the game, the control evolution exhibits various striking and diverse qualitative features. In some cases, the strategy of choosing actions associated with one step Nash equilibria yields a limit cycle response. This confirms observations by other researchers that the temporal evolution of games need not converge to a single Nash equilibrium and opens opportunities for future analysis on making the correct choice of cost functions by determining the effects this has on the agents ability to obtain a desired goal.

Pricing a Protest: Forecasting the Dynamics of Civil Unrest Activity in Social Media.

Online social media activity can often be a precursor to disruptive events such as protests, strikes, and “occupy” movements. We have observed that such civil unrest can galvanize supporters through social networks and help recruit activists to their cause. Understanding the dynamics of social network cascades and extrapolating their future growth will enable an analyst to detect or forecast major societal events. Existing work has primarily used structural and temporal properties of cascades to predict their future behavior. But factors like societal pressure, alignment of individual interests with broader causes, and perception of expected benefits also affect protest participation in social media. Here we develop an analysis framework using a differential game theoretic approach to characterize the cost of participating in a cascade, and demonstrate how we can combine such cost features with classical properties to forecast the future behavior of cascades. Using data from Twitter, we illustrate the effectiveness of our models on the “Brazilian Spring” and Venezuelan protests that occurred in June 2013 and November 2013, respectively. We demonstrate how our framework captures both qualitative and quantitative aspects of how these uprisings manifest through the lens of tweet volume on Twitter social media.

A sensor reduction technique using Bellman optimal estimates of target agent dynamics

Reducing the number of sensors in a sensor network is of great interest for a variety of surveillance and target tracking scenarios. The time and resources needed to process the data from additional sensors can delay reaction time to immediate threats and consume extra financial resources. There are many methods to reduce the number of sensors by considering hardware capabilities alone. However, by incorporating an estimate of environment and agent dynamics, sensor reduction for a given scenario may be achieved using Bellman optimality principles. We propose a method that determines the capture regions where sensors can be eliminated. A capture region is defined as a section of the surveillance field, where using a causal relationship to the other sensors, an event may be determined using fast marching semi-Lagrangian (FMSL) solution techniques. This method is applied to a crowded hallway scenario with two possible exits, one primary, and one alternate. It is desired to determine if a target deviates from the crowd and moves toward the alternate exit. A proximity sensor grid is placed above the crowd to record the number of people that pass through the hallway. Our result shows that the Bellman optimal approximation of the capture set for the alternate exit identifies the region of the surveillance field where sensors are needed, allowing the others to be removed.

Adaptive fuzzy control of switched objective functions in pursuit-evasion scenarios

In recent efforts, the authors have derived simple switched control schemes that qualitatively yield an attractive performance in two player pursuit-evasion games. A drawback of these methods is that detailed knowledge of an opponents dynamics and strategy is required to implement the switching controller. Furthermore, an objective evaluated over a finite horizon may not guide an agent to the target set. To circumvent this potential shortcoming, a switching scheme is proposed where an adaptive fuzzy controller chooses the best objective function from a predefined library to increase the agents reachability. The methodology we present builds on the common approximate dynamic programming reinforcement learning technique. We give conditions for showing when the controller is applicable and give an implementation example with the Homicidal Chauffeur problem.

Time-Series Analysis of Blog and Metaphor Dynamics for Event Detection

Open source indicators (OSI) like social media are useful for detecting and forecasting the onset and progression of political events and mass movements such as elections and civil unrest. Recent work has led us to analyze metaphor usage in Latin American blogs to model such events. In addition to being rich in metaphorical usage, these data sources are heterogeneous with respect to their time-series behavior in terms of publication frequency and metaphor occurrence that make relative comparisons across sources difficult. We hypothesize that understanding these non-normal behaviors is a compulsory step toward improving analysis and forecasting ability. In this work, we discuss our blog data set in detail, and dissect the data along several key characteristics such as blog publication frequency, length, and metaphor usage. In particular, we focus on occurrence clustering: modeling variations in the incidence of both metaphors and blogs over time. We describe these variations in terms of the shape parameters of distributions estimated using maximum likelihood methods. We conclude that although there may be no “characteristic” behavior in the heterogeneity of the sources, we can form groups of blogs with similar behaviors to improve detection ability.

Event Detection from Blogs Using Large Scale Analysis of Metaphorical Usage

Metaphors shape the way people think, decide, and act. We hypothesize that large-scale variations in metaphor usage in blogs can be used as an indicator of societal events. To this end, we use metaphor analysis on a massive scale to study blogs in Latin America over a period ranging from 2000–2015, with most of our data occurring within a nine-year period. Using co-clustering, we form groups of similar behaving metaphors for Argentina, Ecuador, Mexico, and Venezuela and characterize overrepresented as well as underrepresented metaphors for specific locations. We then focus on the metaphor’s potential relation to events by studying the tobacco tax increase in Mexico from 2009–2011. We study correspondences between changes in metaphor frequency with event occurrences, as well as the effect of temporal scaling of data windows on the frequency relationship between metaphors and events.

Sensor reduction technique using Bellman optimal estimates of target agent dynamics

A generalized sensor reduction technique is developed for a sensor network used in surveillance and target tracking operations. Reducing the number of sensors in the network leads to addressing immediate threats more quickly and lowering costs for acquiring and processing data. The methods in this work use Bellman optimality principles to estimate possible paths of an agent given an assumed environment model. These paths are then used to determine causal relationships between states in a surveillance field. By using this approach, a capture set is defined where the final states of trajectories are known using information from sensors located in other states. Sensors can then be removed from the network based on this capture set. This method is applied to a crowded hallway surveillance scenario where an agent may choose between two possible exits. The sensor network in this scenario determines if a target deviates from the crowd and moves toward an alternate exit. A proximity sensor grid is placed above the crowd to record the number of people that pass through the hallway. Our result shows that the Bellman optimal approximation of the capture set for the alternate exit identifies the region of the surveillance field where sensors are needed, allowing the others to be removed. Using the reduced sensor network, results are given that show the probability of a deviating agent becoming more distinct with respect to normal motion of the crowd. Therefore, we conclude that by incorporating a dynamic model of the agents’ motion into the sensor network, sensors can be reduced, and increased detectability is noticed when sensors are removed early in a trajectory of interest.