João P. Hespanha

David Grimsman, Mohd. Shabbir Ali, João P. Hespanha et al.

The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm is implemented in a distributed way, agents sequentially make decisions based on the decisions of all previous agents. This work explores how limited access to the decisions of previous agents affects the quality of the solution of the greedy algorithm. Specifically, we provide tight upper and lower bounds on how well the algorithm performs, as a function of the information available to each agent. Intuitively, the results show that performance roughly degrades proportionally to the size of the largest group of agents which make decisions independently. Additionally, we consider the case where a system designer is given a set of agents and a global limit on the amount of information that can be accessed. Our results show that the best designs partition the agents into equally-sized sets and allow agents to access the decisions of all previous agents within the same set.

Abram H. Clark, Liraz Mudrik, Colton Kawamura et al.

Designing autonomous drone swarms is hampered by a vast design space spanning platform, algorithmic, and numerical-strength choices. We perform large-scale agent-based simulations in three canonical scenarios: swarm-on-swarm battle, cooperative area search with attrition, and pursuit of scattering targets. We demonstrate how dimensional-analysis and data-scaling can be leveraged to collapse performance data onto scaling functions that are mathematically simple, yet counterintuitive and therefore difficult to predict a priori. These scaling laws reveal success-failure boundaries, including sharp break points which we show can be framed as an ``effective swarm size.'' Additionally, we show how this technique can be used to quantify trade-offs between agent count and platform parameters such as velocity, sensing or weapon range, and attrition rate. Furthermore, we show the benefits of embedding an optimal path planning loop within this framework, which can qualitatively improve the scaling laws that govern the outcome. The methods we demonstrate are highly flexible and would enable rapid, budget-aware sizing and algorithm selection for large autonomous swarms.

Asutay Ozmen, João P. Hespanha, Katie Byl

Accurately modeling friction in robotics remains a core challenge, as robotics simulators like Mujoco and PyBullet use simplified friction models or heuristics to balance computational efficiency with accuracy, where these simplifications and approximations can lead to substantial differences between simulated and physical performance. In this paper, we present a physics-informed friction estimation framework that enables the integration of well-established friction models with learnable components-requiring only minimal, generic measurement data. Our approach enforces physical consistency yet retains the flexibility to adapt to real-world complexities. We demonstrate, on an underactuated and nonlinear system, that the learned friction models, trained solely on small and noisy datasets, accurately simulate dynamic friction properties and reduce the sim-to-real gap. Crucially, we show that our approach enables the learned models to be transferable to systems they are not trained on. This ability to generalize across multiple systems streamlines friction modeling for complex, underactuated tasks, offering a scalable and interpretable path toward bridging the sim-to-real gap in robotics and control.

Matthew R. Kirchner, Mark J. Debord, João P. Hespanha

We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the formation are not assigned a priori and a key challenge is to find the optimal configuration assignment along with the optimal control and trajectory. Commonly, assignment and trajectory planning problems are solved separately. We introduce a new multi-vehicle coordination paradigm, where the optimal goal assignment and optimal vehicle trajectories are found simultaneously from a viscosity solution of a single Hamilton-Jacobi (HJ) partial differential equation (PDE), which provides a necessary and sufficient condition for global optimality. Intrinsic in this approach is that individual vehicle dynamic models need not be the same, and therefore can be applied to heterogeneous systems. Numerical methods to solve the HJ equation have historically relied on a discrete grid of the solution space and exhibits exponential scaling with system dimension, preventing their applicability to multiple vehicle systems. By utilizing a generalization of the Hopf formula, we avoid the use of grids and present a method that exhibits polynomial scaling in the number of vehicles.