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We prove the second order differentiation formula along geodesics in finite-dimensional $RCD(K,N)$ spaces. Our approach strongly relies on the approximation of $W_2$-geodesics by entropic interpolations and, in order to implement this…
We demonstrate when and how an entire left-infinite orbit of an underlying dynamical system or observations from such left-infinite orbits can be uniquely represented by a pair of elements in a different space, a phenomenon which we call…
It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD),…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
Although strain-based models have been widely adopted in robotics, no comparison beyond the uniform bending test is commonly recognized to assess their performance. In addition, the increasing effort in prototyping continuum robots…
In this work, we present a method to perform Model Predictive Control (MPC) over systems whose state is an element of $SO(n)$ for $n=2,3$. This is done without charts or any local linearization, and instead is performed by operating over…
We propose a simple, geometrically-motivated construction of smooth random paths in the plane. The construction is such that, with probability one, the paths have finite curvature everywhere (and the realizations are visually pleasing when…
In this work, we explore a data-driven learning-based approach to learning the kinodynamic model of a small autonomous vehicle, and observe the effect it has on motion planning, specifically autonomous drifting. When executing a motion plan…
Sampling-based kinodynamic motion planners (SKMPs) are powerful in finding collision-free trajectories for high-dimensional systems under differential constraints. Time-informed set (TIS) can provide the heuristic search domain to…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based…
We study polynomial random dynamical systems with complete connections on the Riemann sphere. In this framework, the choice of the next polynomial map is governed by a state-dependent rule with memory, extending both i.i.d. random dynamics…
In this paper, we present a task space-based local motion planner that incorporates collision avoidance and constraints on end-effector motion during the execution of a task. Our key technical contribution is the development of a novel…
Task and Motion Planning (TAMP) integrates high-level task planning with low-level motion feasibility, but existing methods are costly in long-horizon problems due to excessive motion sampling. While LLMs provide commonsense priors, they…
Water scarcity has required constant water recycling, leading to a decline in water quality, further exacerbated by high concentrations of fine particles that reduce the efficiency of solid-liquid separation systems. Inclined settlers offer…
Reinforcement Learning (RL) algorithms have shown tremendous success in simulation environments, but their application to real-world problems faces significant challenges, with safety being a major concern. In particular, enforcing…
In this paper, we address the problem of 6-DoF object pose estimation from a single RGB image. Indirect methods that typically predict intermediate 2D keypoints, followed by a Perspective-n-Point solver, have shown great performance. Direct…
Autonomous driving has long grappled with the need for precise absolute localization, making full autonomy elusive and raising the capital entry barriers for startups. This study delves into the feasibility of local trajectory planning for…
This work focuses on pose-following, a variant of path-following in which the goal is to steer the system's position and attitude along a path with a moving frame attached to it. Full body motion control, while accounting for the additional…