Related papers: Necessary and sufficient condition for a generic 3…
In order to make robots more useful in a variety of environments, they need to be highly portable so that they can be transported to wherever they are needed, and highly storable so that they can be stored when not in use. We propose…
Robots with very limited capabilities are placed on the vertices of a graph and are required to move toward a single, common vertex, where they remain stationary once they arrive. This task is referred to as the GATHERING problem. Most of…
Modular robots can be tailored to achieve specific tasks and rearranged to achieve previously infeasible ones. The challenge is choosing an appropriate design from a large search space. In this work, we describe a framework that…
A single nonholonomic under-actuated mobile robot with a bounded control range travels in a 3D workspace. This workspace also hosts a compact unknown domain with a smooth boundary. The robot has access to the horizontal distance to this…
Most of the quadrupeds developed are highly actuated, and their control is hence quite cumbersome. They need advanced electronics equipment to solve convoluted inverse kinematic equations continuously. In addition, they demand special and…
In this paper we obtain a formula for the number of rational degree d curves in $\mathbb{P}^3$ having a cusp, whose image lies in a $\mathbb{P}^2$ and that passes through $r$ lines and $s$ points (where $r + 2s = 3d + 1$). This problem can…
Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected…
Modular small-scale robots offer the potential for on-demand assembly and disassembly, enabling task-specific adaptation in dynamic and constrained environments. However, existing modular magnetic platforms often depend on workspace…
The \textsc{Mutual Visibility} is a well-known problem in the context of mobile robots. For a set of $n$ robots disposed in the Euclidean plane, it asks for moving the robots without collisions so as to achieve a placement ensuring that no…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
We present a probabilistic approach for building, on the fly, 3-D models of unknown objects while being manipulated by a robot. We specifically consider manipulation tasks in piles of clutter that contain previously unseen objects. Most…
A closed convex conic subset $\mathcal{S}$ of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of $\mathcal{S}$ is closely related to the…
For successful object manipulation with robotic hands, it is important to ensure that the object remains in the grasp at all times. In addition to grasp constraints associated with slipping and singular hand configurations, excessive…
In adult laparoscopy, robot-aided surgery is a reality in thousands of operating rooms worldwide, owing to the increased dexterity provided by the robotic tools. Many robots and robot control techniques have been developed to aid in more…
It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a…
We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. We apply…
We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving…
Optimal path planning problems for rigid and deformable (bendable) cuboid robots are considered by providing an analytic safety constraint using generalized $L_p$ norms. For regular cuboid robots, level sets of weighted $L_p$ norms generate…
Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on the position or pose of one or more end-effectors. For robots with redundant degrees of freedom, there is often an infinite, nonconvex…
This paper analyses the workspace of the three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. These manipulators are classified into different groups with similar kinematic properties. The…