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Introduction Goals Overview of Approach Relevent Publications Contact Information

Introduction

The focus of this work is on modeling the interaction dynamics of mobile robotic systems, i.e., modeling properties of the situated system that arise or evolve during execution as a result of the interaction between the robot(s) and the environment. In particular, we explore on-line modeling (i.e., modeling occurring within the lifetime of a task) in the stochastic and uncertain domain of physically embodied single-robot and multi-robot systems.

Our approach employs Augmented Markov Models (AMMs), a technique we have developed based on semi-Markov chains, but having additional statistics associated with links and nodes. We have developed an algorithm that constructs AMMs with little computational overhead, making it feasible for real-time applications (i.e., within the lifetime of a task). We have demonstrated AMMs in a number of robotics applications: fault detection, affiliation determination, hierarchy restructuring, regime detection, and reward maximization. The AMM-based evaluations used in these applications include statistical hypothesis tests and expectation calculations from Markov chain theory. Each of the applications is experimentally verified using up to four physical mobile robots performing elements of a foraging (collection) task.

The encompassing theme in this work is to provide pragmatic and theoretically sound, general-purpose tools for improving the performance of mobile robotic systems.

Goals

The goals of this project are:

  1. To model on-line the interaction dynamics between a real-world robot and its environment.
  2. To use the models in exploring applications not currently addressed in the literature.

Overview of Approach

Augmented Markov Models (AMMs)
Augmented Markov Models are essentially probabilistic finite state machines augmented with statistics on link and node usage. In particular, an AMM is a subclass of semi-Markov chain. Our model construction algorithm is also able to capture the hidden state associated with second (and higher) order transitions. Below we describe the implementation of AMMs and the model construction algorithm. An AMM is a 5-tuple < S,A,B,L,T >

  1. S, a set of symbols {s1, s2, . . . , sM} recognized by the network.

  2. A, a set of states (or nodes) {a1, a2, . . . , aN}, each having four attributes:
    • ais, the symbol recognized by the state.
    • aim, average time steps spent in the state.
    • ais2, variance associated with aim.
    • aip, probability of remaining in ai in the next time step.

  3. B, an N by M transition matrix, where bi,k is the next state given ai and sk.

  4. L, a set of directed links {l1, l2, . . . , lP}, having six attributes:
    • lif, state from which the link begins.
    • lit, state to which the link connects.
    • lid, number of times the link has been traversed.
    • liS, total time spent in lit, after first traversing the link.
    • liS2, sum of squares of durations comprising liS.
    • lip, probability of using the link, given the system is in state lif.

  5. T, a set of elements {t1, t2, . . . , tQ}, each storing data on a two-link transition entering and leaving a state, and having five attributes:
    • tie, the link entering the state.
    • til, the link leaving the state.
    • tid, the number of times ti has been traversed.
    • tiS, total time steps spent in the state that til connects to, after first traversing ti. tiS2, sum of squares of durations comprising tiS.

Characteristics of AMMs:

Model use with mobile robots:
At each time step, the input symbol to the AMM uniquely represents a particular subset of the robot's active behaviors. AMM Construction Algorithm A stream of symbols belonging to S provides the data for model construction. Let sym be the current input symbol, oldsym the previous input symbol, and ac the current state. For each input symbol do:


if sym == oldsym then
   remain in ac and update aip and the appropriate lS, lp, and tS 

else 
   if  sym is in S then
      S = S  unioned with {sym} 
      create a new state ai with ais = sym
      add the new transition to B

   endif
   create a link from ac to the new state if necessary
   create the two-link transition in T if necessary
   update acm, acs2, and ld, lS, lS2, lp, td, tS, tS2 as appropriate 
   do node-splitting if necessary
   transition to the new state
endif

Node-splitting:
For the current state, calculate the binomial mean and variance for transitions in T with the same in-link. If this mean is an outlier, then split the current state and attach the current in-link (with its associated out-links, as indicated in T) to the new state. Using T, make all probabilities consistent. Update T.

AMM Applications:

Fault Detection:

  • Focus on faults that keep the robot in one AMM state: sensor failures, actuator failures, robot becoming physically impeded.
  • A statistical confidence interval for the mean time in a state signals outliers as potential faults.

Group Affiliation:

  • In order to coordinate activity, robots may need to determine whether they are behaviorally identical.
  • Isomorphic AMMs indicate that the robots perform identical tasks.
  • Similar AMM transition probabilities indicate comparable experiences in performing the task.

Dynamic Leader Selection:

  • Dynamically reorganize a group hierarchy to make the best performing robot the leader.
  • Important when the capabilities of the robots are not known or may change due, for example, to failures.
  • Performance data is extracted from AMMs.

Regime Detection:

  • Detect when there is a significant shift in the global environment that may necessitate a change in the robot's behavior.
  • Challenges: robot has no a priori data about the environment and is limited to local sensing.

Reward Maximization:

  • The robot must perform optimally in a stochastic, non-stationary environment.
  • Challenges: robot must estimate environmental state with no a priori data, and with only limited local sensing. Additionally, the non-stationarity of the environment may range from an abrupt change to a gradual shift.

Experimental Task: Foraging

Relevant Publications
Contact Details

For more information contact Maja Mataric'.