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In this paper, we try to understand what people mean when they say that two objects are "similar." This is an important question in the area of human-robot interactions, where robots must interpret human movements in order to act in a "similar" manner. Specifically, we assume that we are given a collection of empirically generated pairwise comparisons between a subset of so-called alternatives (members of a given set), which produces a partial order over the set of alternatives. Based on this partial order, an inverse optimization problem is solved, producing a cost associated with each alternative that is consistent with the partial order. This cost is, moreover, assumed to be generative in that it can be used to select the globally best alternative. An experimental study involving the comparison of apples and oranges is presented to highlight the operation of the proposed approach.

Using graphs and simplicial complexes as models for an environment containing a large number of agents, we provide distributed algorithms based on the HelmholtzHodge decomposition that, given desired flow rates on edges or across faces, produce incompressible approximations to the specified flows. These flows are then "lifted" to produce hybrid controllers for the agents, and a related algorithm is described that computes continuous streamfunctions over the environment, also in a distributed way.

Model predictive control can be computationally intensive as it has to compute an optimal control trajectory at each time instant. As such, we present a method in which parametrized behaviors are introduced as a level of abstraction to give a finite representation to the control trajectory optimization. As these control laws can be designed to accomplish different tasks, the robot is able to use the presented framework to tune the parameters online to achieve desirable results. Moreover, we build on switch-time optimization techniques to allow the model predictive control framework to optimize over a series of given behaviors, allowing for an added level of adaptability. We illustrate the utility of the framework through the control of a nonholonomic mobile robot.