Quantitative Analysis of Molecular Transport in the Extracellular Space Using Physics-Informed Neural Network

The brain extracellular space (ECS), an irregular, extremely tortuous nanoscale space located between cells or between cells and blood vessels, is crucial for nerve cell survival. It plays a pivotal role in high-level brain functions such as memory, emotion, and sensation. However, the specific form of molecular transport within the ECS remain elusive. To address this challenge, this paper proposes a novel approach to quantitatively analyze the molecular transport within the ECS by solving an inverse problem derived from the advection-diffusion equation (ADE) using a physics-informed neural network (PINN). PINN provides a streamlined solution to the ADE without the need for intricate mathematical formulations or grid settings. Additionally, the optimization of PINN facilitates the automatic computation of the diffusion coefficient governing long-term molecule transport and the velocity of molecules driven by advection. Consequently, the proposed method allows for the quantitative analysis and identification of the specific pattern of molecular transport within the ECS through the calculation of the Peclet number. Experimental validation on two datasets of magnetic resonance images (MRIs) captured at different time points showcases the effectiveness of the proposed method. Notably, our simulations reveal identical molecular transport patterns between datasets representing rats with tracer injected into the same brain region. These findings highlight the potential of PINN as a promising tool for comprehensively exploring molecular transport within the ECS.

Learning Diverse Skills for Local Navigation under Multi-constraint Optimality

Despite many successful applications of data-driven control in robotics, extracting meaningful diverse behaviors remains a challenge. Typically, task performance needs to be compromised in order to achieve diversity. In many scenarios, task requirements are specified as a multitude of reward terms, each requiring a different trade-off. In this work, we take a constrained optimization viewpoint on the quality-diversity trade-off and show that we can obtain diverse policies while imposing constraints on their value functions which are defined through distinct rewards. In line with previous work, further control of the diversity level can be achieved through an attract-repel reward term motivated by the Van der Waals force. We demonstrate the effectiveness of our method on a local navigation task where a quadruped robot needs to reach the target within a finite horizon. Finally, our trained policies transfer well to the real 12-DoF quadruped robot, Solo12, and exhibit diverse agile behaviors with successful obstacle traversal.

Diverse Offline Imitation via Fenchel Duality

There has been significant recent progress in the area of unsupervised skill discovery, with various works proposing mutual information based objectives, as a source of intrinsic motivation. Prior works predominantly focused on designing algorithms that require online access to the environment. In contrast, we develop an \textit{offline} skill discovery algorithm. Our problem formulation considers the maximization of a mutual information objective constrained by a KL-divergence. More precisely, the constraints ensure that the state occupancy of each skill remains close to the state occupancy of an expert, within the support of an offline dataset with good state-action coverage. Our main contribution is to connect Fenchel duality, reinforcement learning and unsupervised skill discovery, and to give a simple offline algorithm for learning diverse skills that are aligned with an expert.

RL + Model-based Control: Using On-demand Optimal Control to Learn Versatile Legged Locomotion

This letter presents a versatile control method for dynamic and robust legged locomotion that integrates model-based optimal control with reinforcement learning (RL). Our approach involves training an RL policy to imitate reference motions generated on-demand through solving a finite-horizon optimal control problem. This integration enables the policy to leverage human expertise in generating motions to imitate while also allowing it to generalize to more complex scenarios that require a more complex dynamics model. Our method successfully learns control policies capable of generating diverse quadrupedal gait patterns and maintaining stability against unexpected external perturbations in both simulation and hardware experiments. Furthermore, we demonstrate the adaptability of our method to more complex locomotion tasks on uneven terrain without the need for excessive reward shaping or hyperparameter tuning.

Haptic Teleoperation of High-dimensional Robotic Systems Using a Feedback MPC Framework

Model Predictive Control (MPC) schemes have proven their efficiency in controlling high degree-of-freedom (DoF) complex robotic systems. However, they come at a high computational cost and an update rate of about tens of hertz. This relatively slow update rate hinders the possibility of stable haptic teleoperation of such systems since the slow feedback loops can cause instabilities and loss of transparency to the operator. This work presents a novel framework for transparent teleoperation of MPC-controlled complex robotic systems. In particular, we employ a feedback MPC approach and exploit its structure to account for the operator input at a fast rate which is independent of the update rate of the MPC loop itself. We demonstrate our framework on a mobile manipulator platform and show that it significantly improves haptic teleoperation's transparency and stability. We also highlight that the proposed feedback structure is constraint satisfactory and does not violate any constraints defined in the optimal control problem. To the best of our knowledge, this work is the first realization of the bilateral teleoperation of a legged manipulator using a whole-body MPC framework.