Curriculum-based humanoid robot identification using large-scale human motion database.

Identifying an accurate dynamics model remains challenging for humanoid robots. The difficulty is mainly due to the following two points. First, a good initial model is required to evaluate the feasibility of motions for data acquisition. Second, a highly nonlinear optimization problem needs to be solved to design movements to acquire the identification data. To cope with the first point, in this paper, we propose a curriculum of identification to gradually learn an accurate dynamics model from an unreliable initial model. For the second point, we propose using a large-scale human motion database to efficiently design the humanoid movements for the parameter identification. The contribution of our study is developing a humanoid identification method that does not require the good initial model and does not need to solve the highly nonlinear optimization problem. We showed that our curriculum-based approach was able to more efficiently identify humanoid model parameters than a method that just randomly picked reference motions for identification. We evaluated our proposed method in a simulation experiment and demonstrated that our curriculum was led to obtain a wide variety of motion data for efficient parameter estimation. Consequently, our approach successfully identified an accurate model of an 18-DoF, simulated upper-body humanoid robot.

Development of split-force-controlled body weight support (SF-BWS) robot for gait rehabilitation.

This study introduces a body-weight-support (BWS) robot actuated by two pneumatic artificial muscles (PAMs). Conventional BWS devices typically use springs or a single actuator, whereas our robot has a split force-controlled BWS (SF-BWS), in which two force-controlled actuators independently support the left and right sides of the user's body. To reduce the experience of weight, vertical unweighting support forces are transferred directly to the user's left and right hips through a newly designed harness with an open space around the shoulder and upper chest area to allow freedom of movement. A motion capture evaluation with three healthy participants confirmed that the proposed harness does not impede upper-body motion during laterally identical force-controlled partial BWS walking, which is quantitatively similar to natural walking. To evaluate our SF-BWS robot, we performed a force-tracking and split-force control task using different simulated load weight setups (40, 50, and 60 kg masses). The split-force control task, providing independent force references to each PAM and conducted with a 60 kg mass and a test bench, demonstrates that our SF-BWS robot is capable of shifting human body weight in the mediolateral direction. The SF-BWS robot successfully controlled the two PAMs to generate the desired vertical support forces.

Implicit Contact Dynamics Modeling With Explicit Inertia Matrix Representation for Real-Time, Model-Based Control in Physical Environment.

Model-based control has great potential for use in real robots due to its high sampling efficiency. Nevertheless, dealing with physical contacts and generating accurate motions are inevitable for practical robot control tasks, such as precise manipulation. For a real-time, model-based approach, the difficulty of contact-rich tasks that requires precise movement lies in the fact that a model needs to accurately predict forthcoming contact events within a limited length of time rather than detect them afterward with sensors. Therefore, in this study, we investigate whether and how neural network models can learn a task-related model useful enough for model-based control, that is, a model predicting future states, including contact events. To this end, we propose a structured neural network model predictive control (SNN-MPC) method, whose neural network architecture is designed with explicit inertia matrix representation. To train the proposed network, we develop a two-stage modeling procedure for contact-rich dynamics from a limited number of samples. As a contact-rich task, we take up a trackball manipulation task using a physical 3-DoF finger robot. The results showed that the SNN-MPC outperformed MPC with a conventional fully connected network model on the manipulation task.

o-Azophenylboronic Acid-Based Colorimetric Sensors for d-Fructose: o-Azophenylboronic Acids with Inserted Protic Solvent Are the Key Species for a Large Color Change.

Many boronic acid-based chemosensors for saccharides have been developed; however, their detection mechanisms have seldom been studied. In this study, we synthesized 10 o-azophenylboronic acid derivatives (azoBs) and conducted a fundamental study on the reactivity and the sensing mechanism of azoBs, which undergoes a large color change, e.g., from red to yellow, upon a reaction with saccharides. Their pH-independent formation constants were determined by spectrophotometric titration and then converted to the conditional formation constant K' at pH 7.4. A linear free energy relationship was established between log K' and the pKa of azoB. 11B NMR measurements indicate that in aprotic solvents, azoB forms a trigonal planar structure, while in protic solvents, it forms a quasi-tetrahedral structure (azoB-ROH) with a protic solvent molecule (ROH) inserted between the boronic acid moiety and the azo group. In addition, UV-vis spectroscopic studies showed that the color change during the reaction between azoB and d-fructose in ROH was caused by the release of the ROH from azoB-ROH by d-fructose. Based on the findings in this study, we proposed a guideline for designing an azoB-based chemosensor that exhibits high reactivity toward saccharides and a sufficient color change to allow for the visual detection of saccharides.

Reactivity of Boronic Acids toward Catechols in Aqueous Solution.

Fundamental information on the reactivities of boronic acids toward catechols in aqueous solution is required in all the fields dealing with boronic acid. However, comprehensive studies on reactivity are often hindered by so-called "proton ambiguity," which makes it impossible for the rate constants of boronic acid and boronate ion to be determined separately. Herein, we set up two reaction systems without proton ambiguity: (1) Alizarin Red S and (2) Tiron with several boronic acids (RB(OH)2) with different pKas and performed kinetic and equilibrium studies on the reaction systems. It was shown that the logarithms of the rate constants of RB(OH)2 and its conjugate boronate ion (RB(OH)3-) decreased and increased linearly, respectively, with increasing pKa of RB(OH)2 for both systems. Consequently, the reactivities of RB(OH)2 and RB(OH)3- were reversed at high RB(OH)2 pKa. It was also shown that the bulky o- substituents of phenylboronic acids retarded the backward reactions, resulting in enhancement of the formation constants of boronic acid-catechol esters.

Highly Selective Aluminum(III) Ion Sensing with Luminescent Iridium(III) Complexes Bearing a Distorted 2,2'-Bipyridine-3,3'-diol Moiety Utilizing a Rigidified Seven-Membered Chelate Ring.

To create an ion sensor utilizing a rigidified seven-membered chelate ring, we developed two Ir(III) complexes with 2,2'-bipyridine-3,3'-diol (bpy(OH)2, bpydL) ligands as reaction centers, namely Ir1 ([Ir(ppy)2{bpy(O-)(OH)}], ppy = 2-phenylpyridine) and Ir2 ([Ir(bzq)2{bpy(O-)(OH)}], bzq = benzo[h]quinoline), and evaluated their reactivities toward metal ions by spectrophotometry. When they are reacted with Al3+, these complexes exhibit dramatic enhancements in emission intensity (775-fold for Ir1 and 51.0-fold for Ir2) and distinct orange to green changes in emission color. The reactions of Ir1 and Ir2 with Al3+ were found to barely be affected by nearly all common metal ions. We conclude that these high selectivities arise from the high affinities of the (O,O) atoms in bpydL for hard metal ions and the increased strain of the seven-membered chelate ring due to the coordination of bpydL to the Ir(III) center in each complex, which excludes large metal ions out of the chelate ring.

Human-In-The-Loop Control and Task Learning for Pneumatically Actuated Muscle Based Robots.

Pneumatically actuated muscles (PAMs) provide a low cost, lightweight, and high power-to-weight ratio solution for many robotic applications. In addition, the antagonist pair configuration for robotic arms make it open to biologically inspired control approaches. In spite of these advantages, they have not been widely adopted in human-in-the-loop control and learning applications. In this study, we propose a biologically inspired multimodal human-in-the-loop control system for driving a one degree-of-freedom robot, and realize the task of hammering a nail into a wood block under human control. We analyze the human sensorimotor learning in this system through a set of experiments, and show that effective autonomous hammering skill can be readily obtained through the developed human-robot interface. The results indicate that a human-in-the-loop learning setup with anthropomorphically valid multi-modal human-robot interface leads to fast learning, thus can be used to effectively derive autonomous robot skills for ballistic motor tasks that require modulation of impedance.

An optimal control strategy for hybrid actuator systems: Application to an artificial muscle with electric motor assist.

Humans use multiple muscles to generate such joint movements as an elbow motion. With multiple lightweight and compliant actuators, joint movements can also be efficiently generated. Similarly, robots can use multiple actuators to efficiently generate a one degree of freedom movement. For this movement, the desired joint torque must be properly distributed to each actuator. One approach to cope with this torque distribution problem is an optimal control method. However, solving the optimal control problem at each control time step has not been deemed a practical approach due to its large computational burden. In this paper, we propose a computationally efficient method to derive an optimal control strategy for a hybrid actuation system composed of multiple actuators, where each actuator has different dynamical properties. We investigated a singularly perturbed system of the hybrid actuator model that subdivided the original large-scale control problem into smaller subproblems so that the optimal control outputs for each actuator can be derived at each control time step and applied our proposed method to our pneumatic-electric hybrid actuator system. Our method derived a torque distribution strategy for the hybrid actuator by dealing with the difficulty of solving real-time optimal control problems.

Crystal structure of [5-bromo-2-(pyridin-2-yl-κN)phenyl-κC (1)](pentane-2,4-dionato-κ (2) O,O')platinum(II).

The title cyclo-metalated platinum(II) complex with 2-(4-bromo-phen-yl)pyridinato and acetyl-acetonato ligands, [Pt(C11H7BrN)(C5H7O2)], consists of two crystallographically non-equivalent dimers, each stacked by π-π inter-actions with distances of ≃ 3.4 Å. In both dimers, the platinum(II) complexes are arranged anti-parallel to each other. Each complex exhibits a slightly distorted square-planar coordination environment around the central Pt(II) atom. The dihedral angles between two chelate rings including the Pt(II) atom in these complexes are 0.08 (12) and 1.54 (9)°.

Flipping of the coordinated triazine moiety in Cu(I)-L2 and the small electronic factor, κel, for direct outer-sphere cross reactions: syntheses, crystal structures and redox behaviour of copper(II)/(I)-L2 complexes (L = 3-(2-pyridyl)-5,6-diphenyl-1,2,4-triazine).

Six-coordinate [Cu(pdt)2(H2O)2](2+) and four-coordinate [Cu(pdt)2](+) complexes were synthesized and the cross redox reactions were studied in acetonitrile (pdt = 3-(2-pyridyl)-5,6-diphenyl-1,2,4-triazine). Single crystal analyses revealed that [Cu(pdt)2(H2O)2](BF4)2 was of pseudo-D2h symmetry with two axial water molecules and two symmetrically coordinated equatorial pdt ligands, while the coordination structure of [Cu(pdt)2]BF4 was a squashed tetrahedron (dihedral angle = 54.87°) with an asymmetric coordination by two pdt ligands: one pdt ligand was coordinated to Cu(i) through pyridine-N and triazine-N2 while another pdt ligand was coordinated through pyridine-N and triazine-N4, and a stacking interaction between the phenyl ring on one pdt ligand and the triazine ring on another pdt ligand caused the squashed structure and non-equivalent Cu-N bond lengths. The cyclic voltammograms for [Cu(pdt)2(H2O)2](2+) and [Cu(pdt)2](+) in acetonitrile were identical to each other and quasi-reversible. The reduction of [Cu(pdt)2(H2O)2](2+) by decamethylferrocene and the oxidation of [Cu(pdt)2](+) by [Co(2,2'-bipyridine)3](3+) in acetonitrile revealed that both cross reactions were sluggish through a gated process (the structural change took place prior to the electron transfer) accompanied by slow direct electron transfer processes. It was found that the triazine ring of the coordinated pdt ligand rotates around the C-C bond between the triazine and pyridine rings with the kinetic parameters k = 51 ± 5 s(-1) (297.8 K), ΔH(‡) = 6.2 ± 1.1 kJ mol(-1) and ΔS(‡) = -192 ± 4 J mol(-1) K(-1). The electron self-exchange process was directly measured using the line-broadening method: kex = (9.9 ± 0.5) × 10(4) kg mol(-1) s(-1) (297.8 K) with ΔH(‡) = 44 ± 7 kJ mol(-1) and ΔS(‡) = 0.2 ± 2.6 J mol(-1) K(-1). By comparing this rate constant with the self-exchange rate constants estimated from the cross reactions using the Marcus cross relation, the non-adiabaticity (electronic) factors, κel, for the direct electron transfer processes between [Cu(pdt)2](+/2+) and non-copper metal (Fe(2+) and Co(3+)) complexes were estimated as ca. 10(-7), indicating that the electronic coupling between the d orbitals of copper and of non-copper metals is very small.

Universal reaction mechanism of boronic acids with diols in aqueous solution: kinetics and the basic concept of a conditional formation constant.

To establish a detailed reaction mechanism for the condensation between a boronic acid, RB(OH)2, and a diol, H2L, in aqueous solution, the acid dissociation constants (Ka(BL)) of boronic acid diol esters (HBLs) were determined based on the well-established concept of conditional formation constants of metal complexes. The pKa values of HBLs were 2.30, 2.77, and 2.00 for the reaction systems, 2,4-difluorophenylboronic acid and chromotropic acid, 3-nitrophenylboronic acid and alizarin red S, and phenylboronic acid and alizarin red S, respectively. A general and precise reaction mechanism of RB(OH)2 with H2L in aqueous solution, which can serve as a universal reaction mechanism for RB(OH)2 and H2L, was proposed on the basis of (a) the relative kinetic reactivities of the RB(OH)2 and its conjugate base, that is, the boronate ion, toward H2L, and (b) the determined pKa values of HBLs. The use of the conditional formation constant, K', based on the main reaction: RB(OH)2 + H2L (K1)⇌ RB(L)(OH)(-) + H3O(+) instead of the binding constant has been proposed for the general reaction of uncomplexed boronic acid species (B') with uncomplexed diol species (L') to form boronic acid diol complex species (esters, BL') in aqueous solution at pH 5-11: B' + L' (K')⇌ BL'. The proposed reaction mechanism explains perfectly the formation of boronic acid diol ester in aqueous solution.

Relative kinetic reactivity of boronic acid and boronate ion towards Tiron, 2,2'-biphenol, and propylene glycol.

Reaction systems of boronic acid (RB(OH2), R = phenyl or 3-fluorophenyl) with diols and no proton ambiguity were elaborately set up, and kinetic measurements were conducted to elucidate the relative reactivities of RB(OH)2 and RB(OH)3(-). In the reactions of phenylboronic and 3-fluorophenylboronic acids with propylene glycol, the reactivity order was: RB(OH)2 >> RB(OH)3(-), whereas in the reactions of 3-pyridylboronic acid with Tiron and 2,2'-biphenol, the reactivity of RB(OH)2 was comparable to that of RB(OH)3(-). These results are in contrast to those that have been previously reported, and widely accepted for over thirty years, that concluded that the reactivity of RB(OH)3(-) is several orders of magnitude higher than that of RB(OH)2. The reactivity of Tiron with 3-pyridylboronic acid is affected by the protonation of one of its sulfonate groups.

Formation mechanism of 2-methyl-2-buten-1,4-diol and 2-methyl-3-buten-1,2-diol from 2-methyl-1,3-butadiene on a head-to-head pivalamidato-bridged cis-diammineplatinum(III) binuclear complex.

Reactions of a pivalamidato-bridged head-to-head (HH) platinum(III) binuclear complex with 2-methyl-1,3-butadiene (isoprene) and p-styrenesulfonate and of an α-pyrrolidonato-bridged HH platinum(III) binuclear complex with p-styrenesulfonate were studied kinetically using UV-vis spectrophotometry and (1)H NMR spectroscopy, and detailed reaction mechanisms are proposed. Pt(III) binuclear complexes react with p-styrenesulfonate in four successive steps with mechanisms similar to that for an HH α-pyridonato-bridged Pt(III) binuclear complex with p-styrenesulfonate. In the case of isoprene, four steps were observed on the basis of UV-vis spectrophotometry. However, the reaction kinetics for steps 1 and 2 correspond to those for the previous reaction system, and those for steps 3 and 4 do not correspond to those for the previous system or to those observed by using (1)H NMR spectroscopy for the present isoprene system. By using UV-vis spectrophotometry, it was shown that isoprene preferentially π-coordinates to the Pt(N(2)O(2)) atom via the double bond adjacent to the methyl group in step 1. In step 2, a second isoprene molecule π-coordinates to the Pt(N(4)) atom, which is the rate-determining step, followed by nucleophilic attack of a water molecule on the π-coordinated isoprene on the Pt(N(2)O(2)) atom to form two isomeric σ-complexes. In the same step, π-coordinated isoprene on the Pt(N(4)) atom of the σ-complexes is released. This is different from the reaction of the Pt(III) binuclear complexes with other olefins. In step 3, reductive elimination of the σ-complexes occurs to form two diols and the HH pivalamidato-bridged Pt(II) binuclear complex. Finally, acid decomposition of the Pt(II) binuclear complex occurs to form monomers in step 4. From (1)H NMR spectroscopic observations, fast isomerization between σ-complexes and reductive elimination of the σ-complexes occurs in step 3, and isomerization from a 1,4-diol to a 1,2-diol occurs in step 4.

Optimization of conditions for the determination of boron by a ruthenium(II) complex having diol moiety: A mechanistic study.

Two ruthenium(II) complexes, [Ru(bpy)(2)(dhbpy-H(-1))](+) and [Ru(bpy)(2)(dhphen)](2+) (bpy=2,2'-bipyridine, dhbpy=3,3'-dihydroxy-2,2'-bipyridine, dhphen=5,6-dihydroxy-1,10-phenanthroline) were examined for use as a colorimetric reagent for the determination of boron. The reactions of boric acid with these two complexes were thermodynamically and kinetically studied in detail in order to specify the reactive species and to set up optimum condition for the determination of boron. The detailed analysis of the kinetic data for the reaction of the latter water-soluble complex showed that both boric acid and borate ion were reactive in an alkaline solution. The thermodynamically and kinetically optimum pH for the determination of boron was ca. 9 at 25 degrees C. A spectrofluorimetric determination of boron with the latter complex was attempted at 600nm with excitation at 360nm, and at pH 8.9 using CHES (N-cyclohexyl-2-aminoethanesulfonic acid) buffer. It was found that a trace amount of boron as low as ca. 2x10(-5)M ( approximately 1ppm) could be detectable.

Kinetic evidence for high reactivity of 3-nitrophenylboronic acid compared to its conjugate boronate ion in reactions with ethylene and propylene glycols.

The rate constants for a boronate ion were determined for the first time using the reaction systems of 3-nitrophenylboronic acid (3-NO2PhB(OH)2) with ethylene glycol (EG) and propylene glycol (PG) in an alkaline solution: the rate constants (25 degrees C, I = 0.10 M) for the reactions of 3-NO2PhB(OH)3- are 1.2 M(-1) s(-1) (EG) and 1.5 M(-1) s(-1) (PG), which are at least 10(3) times smaller than those for the reactions of 3-NO 2PhB(OH)2 [1.0 x 10(4) M(-1) s(-1) (EG) and 5.8 x 10(3) M(-1) s(-1) (PG)].

Which is reactive in alkaline solution, boronate ion or boronic acid? Kinetic evidence for reactive trigonal boronic acid in an alkaline solution.

That boronic acid is a reactive species toward a diol moiety even in an alkaline solution and that the boronate ion is not very reactive were demonstrated by the estimated upper limit of the rate constants for the reactions of some boronic acids with 2,2'-biphenol and 2,3-dihydroxynaphthalene in a neutral-alkaline solution, which will correct a common misunderstanding in boron chemistry and would renew the idea of effective boronic acid sensor design for carbohydrates.

Kinetic study of thermal Z to E isomerization reactions of azobenzene and 4-dimethylamino-4'-nitroazobenzene in ionic liquids [1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide with R = butyl, pentyl, and hexyl].

Thermal Z to E isomerization reactions of azobenzene and 4-dimethylamino-4'-nitroazobenzene were examined in three ionic liquids of general formula 1-R-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (R = butyl, pentyl, and hexyl). The first-order rate constants and activation energies for the reactions of azobenzene measured in these ionic liquids were consistent with those measured in ordinary organic solvents, which indicated that the slow isomerization through the inversion mechanism with a nonpolar transition state was little influenced by the solvent properties, such as the viscosity and dielectric constant, of ionic liquids. On the other hand, the rate constants and the corresponding frequency factors of the Arrhenius plot were significantly reduced for the isomerization of 4-dimethylamino-4'-nitroazobenzene in ionic liquids compared with those for the isomerization in ordinary organic molecular solvents with similar dielectric properties. Although these ionic liquids are viscous, the apparent viscosity dependence of the rate constant could not be explained either by the Kramers-Grote-Hynes model or by the Agmon-Hopfield model for solution reactions. It is proposed that the positive and the negative charge centers of a highly polar rotational transition state are stabilized by the surrounding anions and cations, respectively, and that the ions must be rearranged so as to form highly ordered solvation shells around the charge centers of the reactant in the transition state. This requirement for the orderly solvation in the transition state results in unusually small frequency factors of 10(4)-10(7) s(-1).

Isomerization reaction of head-to-head alpha-pyridonato-bridged ethylenediaminepalladium(II) binuclear complex, [Pd2(en)2(C5H4NO)2]2+, in aqueous solution.

Head-to-head bis(alpha-pyridonato)-bridged bis(ethylenediamine)dipalladium(ii), HH-[Pd(2)(en)(2)(alpha-pyridonato)(2)](ClO(4))(2), was synthesized and structurally characterized by X-ray crystallography. The (1)H NMR spectra show that the head-to-head (HH) dimer produces the head-to-tail (HT) dimer and monomers ([Pd(en)(alpha-pyridone)(2)](2+), [Pd(en)(H(2)O)(alpha-pyridone)](2+), [Pd(en)(H(2)O)(2)](2+), etc.) in aqueous solution, and the relative amount of dimers to monomers is dependent on the total concentration of the HH dimer dissolved as well as the acidity of the solution. It was found that the formation of the HH and HT dimers from the monomers is fast, and the HT dimer is produced from the HH dimer only via coexisting monomers, i.e., there is no direct isomerization path between the HH and HT dimers. The kinetic analyses for the HH <==>HT isomerization reaction with time-resolved (1)H NMR measurements revealed that the reaction proceeds via first-order kinetics, which was explained based on a relaxation process. The rate determining step for HH <==>HT isomerization is the reaction step between the mono-alpha-pyridone complex and the bis-alpha-pyridone complex, [Pd(en)(H(2)O)(alpha-pyridone)](2+)+alpha-pyridone <==> [Pd(en)(alpha-pyridone)(2)](2+).

Molecular and biochemical characterization of a serine racemase from Arabidopsis thaliana.

A cDNA encoding a homolog of mammalian serine racemase, a unique enzyme in eukaryotes, was isolated from Arabidopsis thaliana and expressed in Escherichia coli cells. The gene product, of which the amino acid residues for binding pyridoxal 5'-phosphate (PLP) are conserved in this as well as mammalian serine racemases, catalyzes not only serine racemization but also dehydration of serine to pyruvate. The enzyme is a homodimer and requires PLP and divalent cations, Ca2+, Mg2+, Mn2+, Fe2+, or Ni2+, at alkaline pH for both activities. The racemization process is highly specific toward L-serine, whereas L-alanine, L-arginine, and L-glutamine were poor substrates. The Vmax/Km values for racemase activity of L- and D-serine are 2.0 and 1.4 nmol/mg/min/mM, respectively, and those values for L- and D-serine on dehydratase activity are 13 and 5.3 nmol/mg/min/mM, i.e. consistent with the theory of racemization reaction and the specificity of dehydration toward L-serine. Hybridization analysis showed that the serine racemase gene was expressed in various organs of A. thaliana.

Precise investigation of the axial ligand substitution mechanism on a hydrogenphosphato-bridged lantern-type platinum(III) binuclear complex in acidic aqueous solution.

Detailed equilibrium and kinetic studies on axial water ligand substitution reactions of the "lantern-type" platinum(III) binuclear complex, [Pt(2)(mu-HPO(4))(4)(H(2)O)(2)](2)(-), with halide and pseudo-halide ions (X(-) = Cl(-), Br(-), and SCN(-)) were carried out in acidic aqueous solution at 25 degrees C with I = 1.0 M. The diaqua Pt(III) dimer complex is in acid dissociation equilibrium in aqueous solution with -log K(h1) = 2.69 +/- 0.04. The consecutive formation constants of the aquahalo complex () and the dihalo complex () were determined spectrophotometrically to be log = 2.36 +/- 0.01 and log = 1.47 +/- 0.01 for the reaction with Cl(-) and log = 2.90 +/- 0.04 and log = 2.28 +/- 0.01 for the reaction with Br(-), respectively. In the kinetic measurements carried out under the pseudo-first-order conditions with a large excess concentration of halide ion compared to that of Pt(III) dimer (C(X)()- >> C(Pt)), all of the reactions proceeded via a one-step first-order reaction, which is a contrast to the consecutive two-step reaction for the amidato-bridged platinum(III) binuclear complexes. The conditional first-order rate constant (k(obs)) depended on C(X)()- as well as the acidity of the solution. From kinetic analyses, the rate-limiting step was determined to be the first substitution process that forms the monohalo species, which is in rapid equilibrium with the dihalo complex. The reaction with 4-penten-1-ol was also kinetically investigated to examine the reactivity of the lantern complex with olefin compounds.