Related papers: Towards Automatic Identification of Globally Valid…
Developing and fielding complex systems requires proof that they are reliably correct with respect to their design and operating requirements. Especially for autonomous systems which exhibit unanticipated emergent behavior, fully…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie…
A common task in robotics is unloading identical goods from a tray with rectangular grid structure. This naturally leads to the idea of programming the process at one grid position only and translating the motion to the other grid points,…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has…
Underactuated robots are characterized by a larger number of degrees of freedom than actuators and if they are designed with a specific mass distribution, they can be controlled by means of differential flatness theory. This structural…
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system,…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the…
We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system of $n$…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We…
The pattern formation task is commonly seen in a multi-robot system. In this paper, we study the problem of forming complex shapes with functionally limited mobile robots, which have to rely on other robots to precisely locate themselves.…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…
This paper presents a method for algebraic fault detection and identification of nonlinear mechanical systems, describing rigid robots, by using an approximation with orthonormal Jacobi polynomials. An explicit expression is derived for the…