Multi-Robot Cooperative Navigation in Crowds: A Game-Theoretic Learning-Based Model Predictive Control Approach

In this paper, we develop a control framework for the coordination of multiple robots as they navigate through crowded environments. Our framework comprises of a local model predictive control (MPC) for each robot and a social long short-term memory model that forecasts pedestrians' trajectories. We formulate the local MPC formulation for each individual robot that includes both individual and shared objectives, in which the latter encourages the emergence of coordination among robots. Next, we consider the multi-robot navigation and human-robot interaction, respectively, as a potential game and a two-player game, then employ an iterative best response approach to solve the resulting optimization problems in a centralized and distributed fashion. Finally, we demonstrate the effectiveness of coordination among robots in simulated crowd navigation.

Social Navigation in Crowded Environments with Model Predictive Control and Deep Learning-Based Human Trajectory Prediction

Crowd navigation has received increasing attention from researchers over the last few decades, resulting in the emergence of numerous approaches aimed at addressing this problem to date. Our proposed approach couples agent motion prediction and planning to avoid the freezing robot problem while simultaneously capturing multi-agent social interactions by utilizing a state-of-the-art trajectory prediction model i.e., social long short-term memory model (Social-LSTM). Leveraging the output of Social-LSTM for the prediction of future trajectories of pedestrians at each time-step given the robot's possible actions, our framework computes the optimal control action using Model Predictive Control (MPC) for the robot to navigate among pedestrians. We demonstrate the effectiveness of our proposed approach in multiple scenarios of simulated crowd navigation and compare it against several state-of-the-art reinforcement learning-based methods.

Cooperative Energy and Time-Optimal Lane Change Maneuvers with Minimal Highway Traffic Disruption

We derive optimal control policies for a Connected Automated Vehicle (CAV) and cooperating neighboring CAVs to carry out a lane change maneuver consisting of a longitudinal phase where the CAV properly positions itself relative to the cooperating neighbors and a lateral phase where it safely changes lanes. In contrast to prior work on this problem, where the CAV "selfishly" only seeks to minimize its maneuver time, we seek to ensure that the fast-lane traffic flow is minimally disrupted (through a properly defined metric). Additionally, when performing lane-changing maneuvers, we optimally select the cooperating vehicles from a set of feasible neighboring vehicles and experimentally show that the highway throughput is improved compared to the baseline case of human-driven vehicles changing lanes with no cooperation. When feasible solutions do not exist for a given maximal allowable disruption, we include a time relaxation method trading off a longer maneuver time with reduced disruption. Our analysis is also extended to multiple sequential maneuvers. Simulation results show the effectiveness of our controllers in terms of safety guarantees and up to 16% and 90% average throughput and maneuver time improvement respectively when compared to maneuvers with no cooperation.

Optimal Transport Based Refinement of Physics-Informed Neural Networks

In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs solvers have been found to suffer from a host of issues: spectral bias in fully-connected architectures, unstable gradient pathologies, as well as difficulties with convergence and accuracy. Current network training strategies are agnostic to dimension sizes and rely on the availability of powerful computing resources to optimize through a large number of collocation points. This is particularly challenging when studying stochastic dynamical systems with the Fokker-Planck-Kolmogorov Equation (FPKE), a second-order PDE which is typically solved in high-dimensional state space. While we focus exclusively on the stationary form of the FPKE, positivity and normalization constraints on its solution make it all the more unfavorable to solve directly using standard PINNs approaches. To mitigate the above challenges, we present a novel training strategy for solving the FPKE using OT-based sampling to supplement the existing PINNs framework. It is an iterative approach that induces a network trained on a small dataset to add samples to its training dataset from regions where it nominally makes the most error. The new samples are found by solving a linear programming problem at every iteration. The paper is complemented by an experimental evaluation of the proposed method showing its applicability on a variety of stochastic systems with nonlinear dynamics.