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We formulate and analyze a three-dimensional model of motion camouflage, a stealth strategy observed in nature. A high-gain feedback law for motion camouflage is formulated in which the pursuer and evader trajectories are described using…
Reflected random walk in higher dimension arises from an ordinary random walk (sum of i.i.d. random variables): whenever one of the reflecting coordinates becomes negative, its sign is changed, and the process continues from that modified…
This paper focuses on training implicit models of infinite layers. Specifically, previous works employ implicit differentiation and solve the exact gradient for the backward propagation. However, is it necessary to compute such an exact but…
Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and…
Many biological active agents respond to gradients of environmental cues by redirecting their motion. Besides the well-studied prominent examples such as photo- and chemotaxis, there has been considerable recent interest in topotaxis, i.e.\…
Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned…
Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…
This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are…
Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…
Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with an alternating aerial and…
A natural approach for reinforcement learning is to predict future rewards by unrolling a neural network world model, and to backpropagate through the resulting computational graph to learn a policy. However, this method often becomes…
Trains are a corner stone of public transport and play an important role in daily life. A challenging task in train operation is to avoid skidding and sliding during fast changes of traction conditions, which can, for example, occur due to…
Under certain circumstances, a swarm of a species of trail-laying ants known as army ants can become caught in a doomed revolving motion known as the death spiral, in which each ant follows the one in front of it in a never-ending loop…
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of…
We report our initial investigations into reliability and path-finding based models and propose future areas of interest. Inspired by broken sidewalks during on-campus construction projects, we develop two models for navigating this…
Climbing is a multifaceted sport that combines physical demands and emotional and cognitive challenges. Ascent styles differ in fall distance with lead climbing involving larger falls than top rope climbing, which may result in different…
A lattice walk model is said to be reluctant if the defining step set has a strong drift towards the boundaries. We describe efficient random generation strategies for these walks.
We consider walks on the edges of the square lattice $\mathbb Z^2$ which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in another direction. We classify these rules according to a…
Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point. We generalize this analysis to the variable-height inverted pendulum (VHIP) and show how it enables 3D…
Legged robots leverage ground contacts and the reaction forces they provide to achieve agile locomotion. However, uncertainty coupled with contact discontinuities can lead to failure, especially in real-world environments with unexpected…