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

Biology, Reproductive Potential and the Impact of Fishing Pressure on the Bluegill Fishery of Pelican Lake, Uintah County, Utah

Certain aspects of the biology of two species of fish, bluegill (Lepomis macrochirus) and largemouth bass (Micropterus salmoides), and the assessment of fishing pressure upon the sport fishery of Pelican Lake, Uintah County, Utah, a 680 ha warmwater lake, were studied between April 1, 1976 and June 30, 1978. The growth rate of bluegills (sexes combined) was fairly rapid; the mean back-calculated total lengths from ages one through nine were 55, 112, 166, 194, 211, 229, 245, 256 and 259 mm. The growth of largemouth bass was 104, 194, 271, 316, 350, 405 and 416 mm total length for ages one through seven for the combined sexes. Male bluegills matured earlier in life than females. Bluegills spawned continually from the first of June to the first of September, although the peak spawning occurred in June of both years. Gonadal weight to body weight ratios (maturity index) were greatest in the first of June for both male and female bluegills. Fecundity estimates ranged from 1 1,102 mature ova for an age II bluegill to 4 6, 281 mature ova for an age V bluegill. Fecundity estimates for largemouth bass ranged from 4,810 mature ova for a II year old to 31, 719 mature ova for a V year old. Largemouth bass spawned primarily in late May in 1976 and early June in 1977. Angler use of the lake was estimated to be 10,054 angler days fished in 1975, culminating a seven-year increase in use, with subsequent declines in angling to 8,001 angler days in 1976 and 5,027 in 1977. A significant winter fishery developed in 1978. Anglers harvested an estimated 58,277, 44,918 and 22,469 bluegills and 5,791, 2,747 and 4,176 largemouth bass in 1975, 1976 and 1977, respectively. Angler catch rates for bluegills in respective years were 1.520, 1.640 and 1.130 fish/hr and 0.204, 0.094 and 0.213 fish/hr for largemouth bass. Bluegill age groups IV and V and largemouth bass age group III composed the majority of angler harvested fish in 1976 and 1977. Age and size composition of angler harvested bluegills indicated no statistically significant change between 1976 and 1977. Bass harvested by anglers in 1977 were significantly greater in weight than those harvested in 1976. The total annual mortality determined from scale analyses of angler harvested fish was 59.9% for bluegill and 71.6% for bass. A significant number of male bluegills was harvested by anglers in June 1977, the period of peak nesting activity. Anglers released 5,158 bluegills in 1977, of which an estimated 11% (565) were lost to hooking mortality. Of various hook sizes used to assess hooking mortality, number 8 regular shank hooks yielded the highest total mortality (18%). The lowest hooking mortality was with number 6 regular shank jig hooks (0%) and where the leader was cut and the hook allowed to remain (0%). Higher mortality of worm-hooked fish was attributed largely to anatomical location of hooking. Of the total (19) bluegill mortalities, 63% were hooked in the esophagus and 37% in the gill/gill arch. Postwinter population sampling in May 1977 indicated the estimated standing crop weight was 40% less than the prewinter standing crop weight in Au gust 1976. A similar loss in standing crop (37%) was noted in weight from August 1977 to June 1978. The greatest loss in numbers was in young-of-the-year bluegill that suffered an estimated 98% overwinter mortality. Midwinter water quality analyses indicated that anoxic conditions occurred from 2.0 m below the ice to the bottom. An increase in hydrogen sulfide levels was also detected. Recommendations for the fishery were (1) adjustment of the daily bag limit for the bluegill sport fishery with fluctuations in angling use; (2) continuation of a creel census from April 1 through July 31 similar to the design used in this study to annually assess angling use, catch rates, total harvest and the size and age composition of this harvest; (3) stomach analyses of potential predators to assess the overwinter mortality of blue gills; (4) retainment of the current bag limit on largemouth bass with future consideration of utilizing a 12-15-in (305-381 mm) total length limit to increase the numbers of larger, older bass in the population; (5) nonrestrictive use of terminal gear by anglers since hooking mortality of bluegills caught and released by anglers in the summer of 1977 was insignificant; (6 ) no size length restrictions on the bluegills retained by anglers; and (7) consideration of purchasing additional water storage from the irrigation company

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

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

Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties

Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties

Wheel Design and Tension Analysis for the Tethered Axel Rover on Extreme Terrain

As the Mars Exploration rovers have reaffirmed, some of the most interesting sites for scientists to explore on planetary surfaces lie in terrains that are currently inaccessible to state-of-the art rovers. We have been developing the Axel rover as a robotic platform to access steep and challenging terrain. We will summarize the recent mechanical upgrades since we introduced the tethered Axel concept last year

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