Motion planning and stochastic control with experimental validation on a planetary rover

Motion planning for planetary rovers must consider control uncertainty in order to maintain the safety of the platform during navigation. Modelling such control uncertainty is difficult due to the complex interaction between the platform and its environment. In this paper, we propose a motion planning approach whereby the outcome of control actions is learned from experience and represented statistically using a Gaussian process regression model. This model is used to construct a control policy for navigation to a goal region in a terrain map built using an on-board RGB-D camera. The terrain includes flat ground, small rocks, and non-traversable rocks. We report the results of 200 simulated and 35 experimental trials that validate the approach and demonstrate the value of considering control uncertainty in maintaining platform safety.

Mechanism based emulation of dynamic simulation models : concept and application in hydrology

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model.

Visualization of predictive distributions for discrete spatial-temporal log Cox processes approximated with MCMC

An important aspect of decision support systems involves applying sophisticated and flexible statistical models to real datasets and communicating these results to decision makers in interpretable ways. An important class of problem is the modelling of incidence such as fire, disease etc. Models of incidence known as point processes or Cox processes are particularly challenging as they are ‘doubly stochastic’ i.e. obtaining the probability mass function of incidents requires two integrals to be evaluated. Existing approaches to the problem either use simple models that obtain predictions using plug-in point estimates and do not distinguish between Cox processes and density estimation but do use sophisticated 3D visualization for interpretation. Alternatively other work employs sophisticated non-parametric Bayesian Cox process models, but do not use visualization to render interpretable complex spatial temporal forecasts. The contribution here is to fill this gap by inferring predictive distributions of Gaussian-log Cox processes and rendering them using state of the art 3D visualization techniques. This requires performing inference on an approximation of the model on a discretized grid of large scale and adapting an existing spatial-diurnal kernel to the log Gaussian Cox process context.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Potential interstellar molecules : Formation of neutral C6CO from C6CO- in the gas phase

Computations at the RCCSD(T)/aug-cc-pVDZ//B3LYP/6-31G* level of theory indicate that neutral C6CO is a stable species. The ground state of this neutral is the singlet cumulene oxide :C=C=C=C=C=C=C=O. The adiabatic electron affinity and dipole moment of singlet C6CO are 2.47 eV and 4.13 D, respectively, at this level of theory. The anion (C6CO)(-.) should be a possible precursor to this neutral. It has been formed by an unequivocal synthesis in the ion source of a mass spectrometer by the S(N)2(Si) reaction between (CH3)(3)Si-C=C-C=C-C=C-CO-CMe3 and F- to form C-=C-C=C-C=C-CO-CMe3 which loses Me3C in the source to form C6CO-.. Charge stripping of this anion by vertical Franck-Condon oxidation forms C6CO, characterised by the neutralisation-reionisation spectrum (-NR+) of C6CO-., which is stable during the timeframe of this experiment (10(-6) s), Copyright (C) 2000 John Wiley & Sons, Ltd.

Generation of two isomers of C5H from the corresponding anions. A theoretically motivated mass spectrometric study

Molecular orbital calculations have predicted the stability of a range of connectivities for the radical C5H potential surface. The most energetically favorable of these include the linear C4CH geometry and two ring-chain structures HC2C3 and C2C3H The corresponding anions are also shown to be theoretically stable, and furthermore, a fourth isomer, C2CHC2, is predicted to be the most stable anion connectivity. These results have motivated experimental efforts. Methodologies for the generation of the non-ring-containing isomeric anions C4CH and C2CHC2 have been developed utilizing negative ion mass spectrometry. The absolute connectivities of the anions have been established using deuterium labeling, charge reversal, and neutralization reionization techniques. The success of the latter experiment confirms theoretical predictions of stability of the corresponding neutral species. This is the first reported observation of the neutral C2CHC2 species that calculations predict to be substantially less stable than the C4CH connectivity but still bound relative to isomerization processes.

Conversion of neutral C2COC2 to C4CO. potential interstellar molecules

Both [C4CO]−· and [C2COC2]−· are formed in the ion source of a VG ZAB 2HF mass spectrometer by the respective processes HO− + Me3Si–CC–CC–CO–CMe3 → [C4CO]−· + Me3SiOH + Me3C·, and Me3Si–CC–CO–CC–SiMe3 + SF6 + e → [C2COC2]−· + 2Me3SiF + SF4. The second synthetic pathway involves a double desilylation reaction similar to that first reported by Squires. The two radical anion isomers produce different and characteristic charge reversal spectra upon collisional activation. In contrast, following collision induced charge stripping, both radical anions produce neutral C4CO as evidenced by the identical neutralisation reionisation (−NR+) spectra. The exclusive rearrangement of C213COC2 to C413CO indicates that 12C–O bond formation is not involved in the reaction. Ab initio calculations (at the RCCSD(T)/aug-cc-pVDZ//B3LYP/6-31G∗ level of theory) have been used to investigate the reaction coordinates on the potential surfaces for both singlet and triplet rearrangements of neutral C2COC2. Singlet C2COC2 is less stable than singlet C4CO by 78.8 kcal mol−1 and requires only 8.5 kcal mol−1 of additional energy to effect conversion to C4CO by a rearrangement sequence involving three C–C ring opening/cyclisation steps.

Generation and characterization of ionic and neutral dihydroxy boron B(OH)(2)(+/0) in the gas phase

The dicoordinated borinium ion, dihydroxyborinium, B(OH)(2)(+) is generated from methyl boronic acid CH3B(OH)(2) by dissociative electron ionization and its connectivity confirmed by collisional activation. Neutralization-reionization (NR) experiments on this ion indicate that the neutral B(OH)(2) radical is a viable species in the gas phase. Both vertical neutralization of B(OH)(2)(+) and reionization of B(OH)(2) in the NR experiment are, however, associated with particularly unfavorable Franck-Condon factors. The differences in adiabatic and vertical electron transfer behavior can be traced back to a particular pi stabilization of the cationic species compared to the sp(2)-type neutral radical. Thermochemical data on several neutral and cationic boron compounds are presented based on calculations performed at the G2 level of theory.

Formation of two isomeric C3HO radicals from charged precursors in the gas phase. Potential interstellar molecules

Theoretical calculations of the C3HO potential surface at the CCSD(T)/aug-cc-pVDu/B3LYP/6-31G* level indicate that the three radicals HCCCO, CCCHO, and (cyclo-C3H)=O are stable, with HCCCO being the most stable of the three. A fourth isomer, CCHCO, is unstable with respect to cyclization to (cyclo-C3H)=O. Two isomers have been prepared by neutralization of charged precursors, formed as follows: (i) HCCCO, by HC drop C-C(O)-O+(H)(Me) --> HC3O+ + MeOH, and (ii) C2CHO, by (a) Me3SiC drop C-CHO + HO- --> C- drop C-CHO + Me3SiOH and (b) C- drop C-CH(OH)-C drop CH --> C- drop C-CHO + C2H2. A comparison of the CR and -NR+ spectra of -C2CHO indicate that C2CHO is (partially) rearranging to an isomer that shows significant formation of CO.(+) in the -NR+ spectrum of the anion. Ab initio calculations indicate that HCCCO is the product of the isomerism and that a proportion of these isomerized neutrals dissociate to CO and C2H. The neutral HCCCO may be formed by (i) synchronous rearrangement of C2CHO and/or (ii) stepwise rearrangement of C2CHO through (cyclo-C3H)=O. The second of these processes should have the higher rate, as it has the lower barrier in the rate-determining step and the higher Arrhenius pre-exponential A factor.

Cumulenic and heterocumulenic anions : potential interstellar species?

A recent theoretical investigation by Terzieva & Herbst of linear carbon chains, C-n where n greater than or equal to 6, in the interstellar medium has shown that these species can undergo efficient radiative association to form the corresponding anions. An experimental study by Barckholtz, Snow & Bierbaum of these anions has demonstrated that they do not react efficiently with molecular hydrogen, leading to the possibility of detectable abundances of cumulene-type anions in dense interstellar and circumstellar environments. Here we present a series of electronic structure calculations which examine possible anionic candidates for detection in these media, namely the anion analogues of the previously identified interstellar cumulenes CnH and Cn-1CH2 and heterocumulenes CnO (where n = 2-10). The extraordinary electron affinities calculated for these molecules suggest that efficient radiative electron attachment could occur, and the large dipole moments of these simple (generally) linear molecules point to the possibility of detection by radio astronomy.

Conversion of linear to rhombic C-4 in the gas phase: A joint experimental and theoretical study

Charge reversal (CR) and neutralization reionization (NR) experiments carried out on a 4-sector mass spectrometer demonstrate that isotopically labeled, linear C-4 anion rearranges upon collisional oxidation. The cations and neutrals formed in these experiments exhibit differing degrees of isotopic scrambling in their fragmentation patterns, indicative of (at least) partial isomerization of both states. Theoretical studies, employing the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G(d) level of theory, favor conversion to the rhombic C-4 isomer on both cationic and neutral potential-energy surfaces with the rhombic structures predicted to be slightly more stable than the linear forms in each case. The combination of experiment with theory indicates that the elusive rhombic C-4 is formed as a cation and as a neutral following charge stripping of linear C-4(-)

Generation of two isomers of C5H from the corresponding anions. A theoretically motivated mass spectrometric study

Molecular orbital calculations have predicted the stability of a range of connectivities for the radical C5H potential surface. The most energetically favorable of these include the linear C4CH geometry and two ring-chain structures HC2C3 and C2C3H The corresponding anions are also shown to be theoretically stable, and furthermore, a fourth isomer, C2CHC2, is predicted to be the most stable anion connectivity. These results have motivated experimental efforts. Methodologies for the generation of the non-ring-containing isomeric anions C4CH and C2CHC2 have been developed utilizing negative ion mass spectrometry. The absolute connectivities of the anions have been established using deuterium labeling, charge reversal, and neutralization reionization techniques. The success of the latter experiment confirms theoretical predictions of stability of the corresponding neutral species. This is the first reported observation of the neutral C2CHC2 species that calculations predict to be substantially less stable than the C4CH connectivity but still bound relative to isomerization processes.

Syntheses of NCN and NC3N from ionic precursors in the gas phase and an unusual rearrangement of neutral NC3N : A joint experimental and theoretical study

Neutral NCN is made in a mass spectrometer by charge stripping of NCN-., while neutral dicyanocarbene NCCCN can be formed by neutralization of either the corresponding anionic and cationic species, NCCCN-. and NCCCN+.. Theoretical calculations at the RCCSD(T)/aug-cc-pVTZ//B3LYP/6-31+G(d) level of theory indicate that the (3)Sigma (-)(g) State of NCCCN is 18 kcal mol(-1) more stable than the (1)A(1) state. While the majority of neutrals formed from either NCCCN-. or NCCCN+. correspond to NCCCN, a proportion of the neutral NCCCN molecules have sufficient excess energy to effect rearrangement, as evidenced by a loss of atomic carbon in the neutralization reionization (NR) spectra of either NCCCN+. and NCCCN-.. C-13 labeling studies indicate that loss of carbon occurs statistically following or accompanied by scrambling of all three carbon atoms. A theoretical study at the B3LYP/6-31+G(d)//B3LYP/6-31+G(d) level of theory indicates that C loss is a consequence of the rearrangement sequence NCCCN --> CNCCN --> CNCNC and that C scrambling occurs within singlet CNCCN via the intermediacy of a four-membered C-2v-symmetrical transition structure.