On the Suitability of Different Online Gait Generation Methods for Pre-Defined Footsteps

Detailed dynamical modeling is the basis for simulation and model based control. In this contribution the Projection Equation is used for the modeling of a biped walking machine, resulting in the equations of motion which are needed for gait generation and verification of its stability. For biped robots one main issue is the generation of stable trajectories for the center of mass (CoM). Several different approaches based on the Zero Moment Point (ZMP) scheme have been presented in the past. Due to the complex dynamic structure of bipedal robots most of the considered algorithms use a linear inverted pendulum as a simplified model. This results in a decoupling of the ZMP equations in lateral and forward direction, but limits the trajectories to a constant height of the CoM. An extension of the well known LQR theory by future reference values has been proposed. This model based approach seems to perform quite well, but does not allow the consideration of constraints on the position of the ZMP. This limitation is removed by the use of Model Predictive Control (MPC) with inequality constraints. By extending this approach to a time invariant one the restriction to a constant height of the CoM is no longer necessary. Both methods as well as the time invariant approach for variable CoM heights have been evaluated in simulations and will be experimentally verified on a real robot soon. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tuning of spin crossover behaviour in iron(III) complexes involving pentadentate Schiff bases and pseudohalides

Investigations on a series of eight novel mononuclear iron(III) Schiff base complexes with the general formula [Fe(L(5))(L(1))]·S (where H(2)L(5) = pentadentate Schiff-base ligand, L(1) = a pseudohalido ligand, and S is a solvent molecule) are reported. Several different aromatic 2-hydroxyaldehyde derivatives were used in combination with a non-symmetrical triamine 1,6-diamino-4-azahexane to synthesize the H(2)L(5) Schiff base ligands. The consecutive reaction with iron(III) chloride resulted in the preparation of the [Fe(L(5))Cl] precursor complexes which were left to react with a wide range of the L(1) pseudohalido ligands. The low-spin compounds were prepared using the cyanido ligand: [Fe(3m-salpet)(CN)]·CH(3)OH (1a), [Fe(3e-salpet)(CN)]·H(2)O (1b), while the high-spin compounds were obtained by the reaction of the pseudohalido (other than cyanido) ligands with the [Fe(L(5))Cl] complex arising from salicylaldehyde derivatives: [Fe(3Bu5Me-salpet)(NCS)] (2a), [Fe(3m-salpet)(NCO)]·CH(3)OH (2b) and [Fe(3m-salpet)(N(3))] (2c). The compounds exhibiting spin-crossover phenomena were prepared only when L(5) arose from 2-hydroxy-1-naphthaldehyde (H(2)L(5) = H(2)napet): [Fe(napet)(NCS)]·CH(3)CN (3a, T(1/2) = 151 K), [Fe(napet)(NCSe)]·CH(3)CN (3b, T(1/2) = 170 K), [Fe(napet)(NCO)] (3c, T(1/2) = 155 K) and [Fe(napet)(N(3))], which, moreover, exhibits thermal hysteresis (3d, T(1/2)↑ = 122 K, T(1/2)↓ = 117 K). These compounds are the first examples of octahedral iron(III) spin-crossover compounds with the coordinated pseudohalides. We report the structure and magnetic properties of these complexes. The magnetic data of all the compounds were analysed using the spin Hamiltonian formalism including the ZFS term and in the case of spin-crossover, the Ising-like model was also applied.     

ent-Homoabyssomicins A and B, two new spirotetronate metabolites from Streptomyces sp. Ank 210

ent-Homoabyssomicins A (1) and B (2) are new complex polycyclic spirotetronate metabolites isolated from Streptomyces sp. isolate Ank 210. The structures of 1 and 2 were elucidated by detailed spectroscopic analyses of 1D and 2D NMR data. The absolute configuration of 1 was established by subsequent single-crystal X-ray diffraction studies.     

Synthesis and characterization of a trinuclear Cu(II)3 complex bridged by an extended phloroglucinol-ligand: implications for a rational enhancement of ferromagnetic interactions

The synthesis and characterization of the extended phloroglucinol-ligand H(3)felden based on the trialdehyde 2,4,6-triformylphloroglucinol and its trinuclear Cu(II)(3) complex [(felden){Cu(bpy)}(3)](ClO(4))(3) is presented. This study is motivated to optimize analogous extended phloroglucinol-ligands based on the triketone 2,4,6-triacetylphloroglucinol, which transmit ferromagnetic interactions by the spin-polarization mechanism between three Cu(II) ions and have therefore been applied as the central ligand backbone for a class of heptanuclear single-molecule magnets in a supramolecular approach. A detailed NMR spectroscopic study reveals that the ligand H(3)felden is not in the usually anticipated enol-imine form but in the tautomeric keto-enamine form. The presence of a C(3h) and a C(s) symmetric isomer results in a set of four different signals for each proton. In conjunction with FTIR, electronic absorption spectroscopy, and bond length considerations, it also appears that the complex [(felden){Cu(bpy)}(3)](ClO(4))(3) must be considered as a resonance hybrid of an enolate-imine and a keto-enamine form. A strong contribution of the keto-enamine resonance structure with loss of the central π system explains the weak but ferromagnetic interactions between the Cu(II)S = 1/2 spins. This detailed analysis identifies the strong resonance with unsaturated groups in 2,4,6-position of phloroglucinol as the main source for the low ferromagnetic couplings by the spin-polarization mechanism in these ligands. This provides a synthetic handle to improve the spin-polarization mechanism in these ligands by replacing the imine with amine functions.     

Fujianmycin C, A bioactive angucyclinone from a marine derived Streptomyces sp. B6219

From a marine-derived streptomycete, a new bioactive angucyclinone, fujianmycin C (1), has been isolated along with five known, metabolites fujianmycins A (2) and B (3), ochromycinone (4), ochromycinone methyl ether (5), and tetrangulol methyl ether (6). The structure elucidation of fujianmycin C (1) was performed by detailed analysis of data such as 1H, 13C, 1H, 1H COSY, HSQC, HMBC and NOESY spectra. Fujianmycin C (1) exhibited antibacterial activity against Streptomyces viridochromogenes (Tü57).     

Do Trinuclear Triplesalen Complexes Exhibit Cooperative Effects? Synthesis,Characterization, and Enantioselective Catalytic Sulfoxidation by Chiral Trinuclear FeIII Triplesalen Complexes

The chiral triplesalen ligand H₆chand provides three chiral salen ligand compartments in a meta‐phenylene arrangement by a phloroglucinol backbone. The two diastereomeric versions H₆chand^RR and H₆chand^rac have been used to synthesize the enantiomerically pure chiral complex [(FeCl)₃(chand^RR)] ( 3^RR ) and the racemic complex [(FeCl)₃(chand^rac)] ( 3^rac ). The molecular structure of the free ligand H₆chand^rac exhibits at the terminal donor sides the O‐protonated phenol–imine tautomer and at the central donor sides the N‐protonated keto–enamine tautomer. The trinuclear complexes are comprised of five‐coordinate square‐pyramidal Fe^III ions with a chloride at the axial positions. The crystal structure of 3^rac exhibits collinear chiral channels of ～11 Å in diameter making up 33.6 % of the volume of the crystals, whereas the crystal structure of 3^RR exhibits voids of 560 ų. Mössbauer spectroscopy demonstrates the presence of Fe^III high‐spin ions. UV/Vis spectroscopy is in accordance with a large delocalized system in the central backbone evidenced by strong low‐energy shifts of the imine π–π* transitions relative to that of the terminal units. Magnetic measurements reveal weak intramolecular exchange interactions but strong magnetic anisotropies of the Fe^III ions. Complexes 3^rac and 3^RR are good catalysts for the sulfoxidation of sulfides providing very good yields and high selectivities with 3^RR being enantioselective. A comparison of 3^RR and [FeCl(salen′)] provides higher yields and selectivities but lower enantiomeric excess values (ee values) for 3^RR relative to [FeCl(salen′)]. The low ee values of 3^RR appeared to be connected to a strong ligand folding in 3^RR , opening access to the catalytically active high‐valent Fe–O species. The higher selectivity is assigned to a cooperative stabilization of the catalytically active high‐valent Fe–O species through the phloroglucinol backbone in the trinuclear complexes.     

Energy functionals and soliton equations for G2-forms

We extend short-time existence and stability of the Dirichlet energy flow as proven in a previous article by the authors to a broader class of energy functionals. Furthermore, we derive some monotonely decreasing quantities for the Dirichlet energy flow and investigate an equation of soliton type. In particular, we show that nearly parallel G₂-structures satisfy this soliton equation and study their infinitesimal soliton deformations.     

An inverted triplesalen ligand by a convergent synthesis and its influence on trinuclear FeIII 3 complexes

The inverted triplesalen ligand H 6 feld Me has been synthesized from 2,4,6-triformyl-phloroglucinol and a ketimine salen half-unit in a convergent synthesis. NMR, IR, and UV-vis spectroscopy reveal that this ligand is not in the O-protonated tautomer but in the N-protonated tautomer with substantial heteroradialene contribution. This ligand and the conventional triplesalen ligand H 6 talen t-Bu 2 have been used to synthesize the trinuclear Fe III complexes [(feld Me )(FeCl) 3 ] and [(talen t-Bu 2 )(FeCl) 3 ], respectively. The molecular structures of these complexes were obtained by single-crystal X-ray diffraction. Two trinuclear Fe III complexes of [(feld Me )(FeCl) 3 ] dimerize via two Fe-phenolate bonds, whereas due to steric hindrance no dimerization is observed for [(talen t-Bu 2 )(FeCl) 3 ]. The structural data also reveal some heteroradialene contribution in the trinuclear complexes. Whereas UV-vis and M bauer spectroscopy are not suitable to distinguish between the two complexes, FT-IR spectra show characteristic features due to the different substitution patterns of the conventional and the inverted triplesalen ligands. Another handle is provided by electrochemistry. Whereas both complexes exhibit an irreversible oxidation wave (0.94 V vs. Fc + /Fc for [(feld Me )(FeCl) 3 ] and 0.84 V vs. Fc + /Fc for [(talen t-Bu 2 )(FeCl) 3 ]), which is assigned to the oxidation of the central backbone, higher potential oxidations are reversible for [(talen t-Bu 2 )(FeCl) 3 ]) but irreversible for [(feld Me )(FeCl) 3 ]. This is attributed to the reversible oxidation of the terminal phenolates in the di-tert-butyl substituted [(talen t-Bu 2 )(FeCl) 3 ] in contrast to the mono-methyl-substituted phenolates in [(feld Me )(FeCl) 3 ]. The magnetic properties of [(talen t-Bu 2 )(FeCl) 3 ] reveal a very small ferromagnetic coupling with significant zero-field splitting of the FeⅢ S = 5/2 ions. In contrast, the dimerization of two trinuclear complexes in [(feld Me )(FeCl) 3 ] results in antiferromagnetic interactions between the two phenolate-bridged Fe III ions, which mask the intra-trinuclear interactions transmitted by the central phloroglucinol backbone.