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This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.

In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with contacts employ mode-scheduling, which requires an a priori knowledge of the contact order and thus cannot produce complex or non-intuitive behaviors. Contact-implicit trajectory optimization methods offer a solution to this by allowing the optimization to make or break contacts as needed, but thus far have suffered from poor accuracy. Here, we combine methods from direct collocation using higher order orthogonal polynomials with contact-implicit optimization to generate trajectories with significantly improved accuracy. The key insight is to increase the order of the polynomial representation while maintaining the assumption that impact occurs over the duration of one finite element.

Accurate estimation of surface wettability for various degrees of hydrophobicity becomes increasingly important in the molecular design of membrane. In this paper, we develop simple yet physically realistic model for estimating contact angle via hybridizing molecular dynamics and pseudocontinuum theory. Molecular dynamics simulations were carried out to compute the macro-scale contact angle between a water droplet and smooth walls from the nanoscale calculations. A macro-level droplet including countless degrees of freedom due to an infinite number of molecules is impossible to be studied directly via atomistic simulations. To resolve this issue, we employed two approaches consisting of the pseudocontinuum approximation and the modified Young-Laplace equation. The former involves the 9-3 Lennard-Jones (L-J) potential and can drastically reduce the degrees of freedom in molecular simulations, while the latter relates the mesoscale contact angle to the realistic one. We altered different parameters including the liquid-surface potential characteristics and the temperature, and calculated the water contact angle by leveraging the mass density profile fitting method to predict the broad spectrum of hydrophobic and hydrophilic substrates. The computational results were compared with the experimental data for various materials including graphite, silicon, and metals. This study suggests that pseudocontinuum modeling is an accurate approach to probe surface wettability for various processes at a low computational cost.