An official website of the United States government
We present a new technology-based paradigm to support embodied mathematics educational games, using wearable devices in the form of SmartPhones and SmartWatches for math learning, for full classes of students in formal in- school education settings. The Wearable Learning Games Engine is web based infrastructure that enables students to carry one mobile device per child, as they embark on math team-based activities that require physical engagement with the environment. These Wearable Tutors serve as guides and assistants while students manipulate, measure, estimate, discern, discard and find mathematical objects that satisfy specified constraints. Multi-player math games that use this infrastructure have yielded both cognitive and affective benefits. Beyond math game play, the Wearable Games Engine Authoring Tool enables students to create games themselves for other students to play; in this process, students engage in computational thinking and learn about finite-state machines. We present the infrastructure, games, and results for a series of experiments on both game play and game creation.
more »
« less
Experiments with sensorimotor games in dynamic human/machine interaction
While interacting with a machine, humans will naturally formulate beliefs about the machine's behavior, and these beliefs will affect the interaction. Since humans and machines have imperfect information about each other and their environment, a natural model for their interaction is a game. Such games have been investigated from the perspective of economic game theory, and some results on discrete decision-making have been translated to the neuromechanical setting, but there is little work on continuous sensorimotor games that arise when humans interact in a dynamic closed loop with machines. We study these games both theoretically and experimentally, deriving predictive models for steady-state (i.e. equilibrium) and transient (i.e. learning) behaviors of humans interacting with other agents (humans and machines). Specifically, we consider experiments wherein agents are instructed to control a linear system so as to minimize a given quadratic cost functional, i.e. the agents play a Linear-Quadratic game. Using our recent results on gradient-based learning in continuous games, we derive predictions regarding steady-state and transient play. These predictions are compared with empirical observations of human sensorimotor learning using a teleoperation testbed.
more »
« less
- Award ID(s):
- 1836819
- PAR ID:
- 10111544
- Date Published:
- Journal Name:
- Micro- and Nanotechnology Sensors, Systems, and Applications XI
- Page Range / eLocation ID:
- 81
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract This paper studies the equilibrium price of an asset that is traded in continuous time betweenNagents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The unique equilibrium price is characterized by a weakly coupled system of linear parabolic equations which shows that holding and liquidity costs play dual roles. We derive the leading‐order asymptotics for small transaction and holding costs which give further insight into the equilibrium and the consequences of illiquidity.more » « less
-
In this paper, we address the problem of a two-player linear quadratic differential game with incomplete information, a scenario commonly encountered in multi-agent control, human-robot interaction (HRI), and approximation methods to solve general-sum differential games. While solutions to such linear differential games are typically obtained through coupled Riccati equations, the complexity increases when agents have incomplete information, particularly when neither is aware of the other’s cost function. To tackle this challenge, we propose a model-based Peer-Aware Cost Estimation (PACE) framework for learning the cost parameters of the other agent. In PACE, each agent treats its peer as a learning agent rather than a stationary optimal agent, models their learning dynamics, and leverages this dynamic to infer the cost function parameters of the other agent. This approach enables agents to infer each other’s objective function in real time based solely on their previous state observations and dynamically adapt their control policies. Furthermore, we provide a theoretical guarantee for the convergence of parameter estimation and the stability of system states in PACE. Additionally, using numerical studies, we demonstrate how modeling the learning dynamics of the other agent benefits PACE, compared to approaches that approximate the other agent as having complete information, particularly in terms of stability and convergence speed.more » « less
-
Digital games featuring programmable agents are popular tools for teaching coding and computational thinking skills. However, today's games perpetuate an arguably obsolete relationship between programmable agents and human operators. Borrowing from the field of human-robotics interaction, we argue that collaborative robots, or cobots, are a better model for thinking about computational agents, working directly with humans rather than in place of or at arm's length from them. In this paper, we describe an initial design inquiry into the design of “cobot games”, programmable agent scenarios in which players program an in-game ally to assist them in accomplishing gameplay objectives. We detail three questions that emerged out of this exploration, our present thinking on them, and plans for deepening inquiry into cobot game design moving forward.more » « less
-
We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents interacting in a mean field manner. We reduce the problem to the optimal control of dynamics of the McKean-Vlasov type, and we solve this problem explicitly in a special case reminiscent of the linear - quadratic mean field game models. The paper concludes with a numerical example demonstrating the power of the results when applied to a simple example of epidemic containment.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1117/12.2519258
