The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.Comment: 8 pages and 4 figure

The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices

This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on Se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method

On the Tutte-Krushkal-Renardy polynomial for cell complexes

Recently V. Krushkal and D. Renardy generalized the Tutte polynomial from graphs to cell complexes. We show that evaluating this polynomial at the origin gives the number of cellular spanning trees in the sense of A. Duval, C. Klivans, and J. Martin. Moreover, after a slight modification, the Tutte-Krushkal-Renardy polynomial evaluated at the origin gives a weighted count of cellular spanning trees, and therefore its free term can be calculated by the cellular matrix-tree theorem of Duval et al. In the case of cell decompositions of a sphere, this modified polynomial satisfies the same duality identity as the original polynomial. We find that evaluating the Tutte-Krushkal-Renardy along a certain line gives the Bott polynomial. Finally we prove skein relations for the Tutte-Krushkal-Renardy polynomial..Comment: Minor revision according to a reviewer comments. To appear in the Journal of Combinatorial Theory, Series

Barrier Functions for Multiagent-POMDPs with DTL Specifications

Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time barrier functions (DTBFs) and formulate sufficient conditions for finite time DTBF to study finite time convergence to a set. We then show that different LDTL mission/safety specifications can be cast as a set of invariance or finite time reachability problems. We demonstrate that the proposed method for safety-shield synthesis can be implemented online by a sequence of one-step greedy algorithms. We demonstrate the efficacy of the proposed method using experiments involving a team of robots

Smooth feedback control algorithms for distributed manipulators

This paper introduces a smooth control algorithm for controlling fully actuated distributed manipulation systems that operate by frictional contact. The control law scales linearly with the number of actuators and is simple to implement. Moreover, we prove that control law has desirable robustness properties in the presence of the nonsmooth mechanics inherent in distributed manipulation systems that rely upon frictional contact. This algorithm has been implemented on an experimental distributed manipulation test-bed, whose structure is briefly reviewed. The experimental results confirm the validity and performance of the algorithm

Time functions appropriate for nuclear explosions

The source-time function of megaton class nuclear explosions has been determined by modeling teleseismic short- and long-period body waves with synthetic seismograms. A simple analytic expression for the time function was used to closely match observations from both Novaya Zemlya and the U.S. test site at Amchitka. It was found that the time functions of all the events have a substantial overshoot. It was also found that, although the durations of the time functions did appear to depend on yield, the effect was very difficult to observe even in short-period records. All synthetics were computed by assuming a simple point source in a layered elastic half-space. It was not necessary to appeal to any nonlinear processes in the source region to explain the observations. Numerical calculations are presented to show that tectonic release triggered by earthquakes does not have a substantial effect on the P waves unless the long-period level of the tectonic event is as large or larger than the long-period level of the explosion. The pS wave, on the other hand, is shown to be very sensitive to even a moderate amount of tectonic release