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We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…
In this paper we attempt to give a systematic account on privileged coordinates and the nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold with a distinguished filtration of subbundles of the tangent…
We study a robot snake model based on a discrete linear control system involving Fibonacci sequence and closely related to the theory of expansions in non-integer bases. The present paper includes an investigation of the reachable…
We investigate the snaking of localised patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, that are not…
Studying snake robot locomotion in a cluttered environment has been a complicated task because the motion model is discontinuous due to the physical contact with obstacles, and the contact force cannot be determined solely by contact…
Despite advances in a diversity of environments, snake robots are still far behind snakes in traversing complex 3-D terrain with large obstacles. This is due to a lack of understanding of how to control 3-D body bending to push against…
We consider a controlled evolution problem for a set $\Omega(t)\in\mathbb{R}^d$, originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficient conditions are given, in order that the evolution be…
In this paper, we study an approximate controllability for the impulsive linear evolution equations in Hilbert spaces. The necessary and sufficient conditions for approximate controllability in terms of resolvent operators are given. An…
Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake…
This paper studies the problem of having mobile robots in a multi-robot system maintain an estimate of the relative position and relative orientation of near-by robots in the environment. This problem is studied in the context of large…
Object manipulation has been extensively studied in the context of fixed base and mobile manipulators. However, the overactuated locomotion modality employed by snake robots allows for a unique blend of object manipulation through…
This work aims to develop a resource-efficient solution for obstacle-avoiding tracking control of a planar snake robot in a densely cluttered environment with obstacles. Particularly, Neuro-Evolution of Augmenting Topologies (NEAT) has been…
Object manipulation has been extensively studied in the context of fixed base and mobile manipulators. However, the overactuated locomotion modality employed by snake robots allows for a unique blend of object manipulation through…
We study the geometry associated with the kinematics of a planar robot known as the "three-segment snake," whose velocity distribution belongs to a class of (2,3,5) distributions. We discover that, under certain assumptions on its…
This work is devoted to the problem of distributed target tracking when a team of robots detect the target through a variable perception-latency mechanism. A reference for the robots to track is constructed in terms of a desired formation…
We propose a function-learning methodology with a control-theoretical foundation. We parametrise the approximating function as the solution to a control system on a reproducing-kernel Hilbert space, and propose several methods to find the…
Snakes can bend their elongate bodies in various forms to traverse various environments. We understand how snakes use lateral bending to push against asperities on flat ground for propulsion, and snake robots can do so effectively. However,…
A controlled sweeping process with prox-regular set, $W^{1,2}$-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong…
We consider the piecewise linear approximation of saddle functions of the form $f(x,y)=ax^2-by^2$ under the L-infinity error norm. We show that interpolating approximations are not optimal. One can get slightly smaller errors by allowing…
Snake robots have the potential to maneuver through tightly packed and complex environments. One challenge in enabling them to do so is the complexity in determining how to coordinate their many degrees-of-freedom to create purposeful…