Yash Kothari

J. Taery Kim, Wenhao Yu, Yash Kothari et al. · gatech

This paper explores the principles for transforming a quadrupedal robot into a guide robot for individuals with visual impairments. A guide robot has great potential to resolve the limited availability of guide animals that are accessible to only two to three percent of the potential blind or visually impaired (BVI) users. To build a successful guide robot, our paper explores three key topics: (1) formalizing the navigation mechanism of a guide dog and a human, (2) developing a data-driven model of their interaction, and (3) improving user safety. First, we formalize the wayfinding task of the human-guide robot team using Markov Decision Processes based on the literature and interviews. Then we collect real human-robot interaction data from three visually impaired and six sighted people and develop an interaction model called the ``Delayed Harness'' to effectively simulate the navigation behaviors of the team. Additionally, we introduce an action shielding mechanism to enhance user safety by predicting and filtering out dangerous actions. We evaluate the developed interaction model and the safety mechanism in simulation, which greatly reduce the prediction errors and the number of collisions, respectively. We also demonstrate the integrated system on a quadrupedal robot with a rigid harness, by guiding users over $100+$~m trajectories.

Qi Zeng, Yash Kothari, Spencer H. Bryngelson et al. · gatech

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy solutions, typically attaining about $0.1\%$ relative error. We present an adversarial approach that overcomes this limitation, which we call competitive PINNs (CPINNs). CPINNs train a discriminator that is rewarded for predicting mistakes the PINN makes. The discriminator and PINN participate in a zero-sum game with the exact PDE solution as an optimal strategy. This approach avoids squaring the large condition numbers of PDE discretizations, which is the likely reason for failures of previous attempts to decrease PINN errors even on benign problems. Numerical experiments on a Poisson problem show that CPINNs achieve errors four orders of magnitude smaller than the best-performing PINN. We observe relative errors on the order of single-precision accuracy, consistently decreasing with each epoch. To the authors' knowledge, this is the first time this level of accuracy and convergence behavior has been achieved. Additional experiments on the nonlinear Schrödinger, Burgers', and Allen-Cahn equation show that the benefits of CPINNs are not limited to linear problems.