configuration flatness of lagrangian control systems with fewer controls than degrees of freedom abstract a lagrangian control system is said to be configuration flat if its states are determined by configuration flat outputs depending on configuration variables only this paper gives a necessary condition and two types of sufficient conditions for lagrangian control systems with n degrees of freedom and m controls with m n to be configuration flat and further makes a remark on the choice of output variables for configuration flatness two examples are given in which the sufficient conditions are utilized for finding configuration flat outputs

the influence of stimulus envelope and fine structure on the binaural masking level difference a masking level difference mld paradigm was used to investigate the influence of stimulus envelope and stimulus fine structure characteristics on monaural and binaural hearing the degree of masker envelope fluctuation was manipulated by selecting narrow band noises 50 hz on a continuum of values of the normalized fourth moment of the envelope the noises were specified as low noise noise lnn medium noise noise mnn and high noise noise hnn fine structure cues were studied by measuring thresholds at 500 and 4000 hz regions in which the availability of such cues to the auditory system differ substantially in addition thresholds were measured for gaussian noise maskers gn and for maskers having a flat magnitude spectrum termed equal magnitude noise emn maskers the results indicated lower noso thresholds for lnn than for the other four masker types furthermore there were no differences in threshold for maskers having moderate and high degrees of envelope fluctuation mnn and hnn the

almost global stabilization of fully actuated rigid bodies this paper addresses the problem of stabilizing a fully actuated rigid body the problem is formulated by considering the natural configuration space for rigid bodies the special euclidean group se 3 the proposed solution consists of a landmark based controller for force and torque actuation that guarantees almost global asymptotic stability of the desired equilibrium point as such the equilibrium point is asymptotically stable and only a nowhere dense set of measure zero lies outside its region of attraction the controller uses velocity measurements and the position coordinates of a collection of landmarks fixed in the environment as an additional feature the control law is designed so as to verify prescribed bounds on the actuation

differential flatness of two one forms in arbitrary number of variables given a differentially flat system of odes flat outputs that depend only on original variables but not on their derivatives are called zero flat outputs and systems possessing such outputs are called zero flat in this paper we present a theory of zero flatness for a system of two one forms in arbitrary number of variables t x1 xn our approach splits the task of finding zero flat outputs into two parts first part involves solving for distributions that satisfy a set of algebraic conditions the second part involves finding an integrable distribution from the solution set of the first part typically this part involves solving pdes our results are also applicable in determining if a control affine system in n states and n 2 controls has flat outputs that depend only on states we illustrate our method by examples

brief paper vision based control for rigid body stabilization this paper addresses the problem of stabilizing to a desired equilibrium point an eye in hand system which consists of a single camera mounted on a rigid body free to move on se 3 it is assumed that there is a collection of landmarks fixed in the environment and that the image coordinates of those landmarks are provided to the system by an on board ccd camera the proposed method addresses not only the problem of stabilization but also that of maintaining feature visibility along the system s trajectory the resulting solution consists of a feedback control law based on the current and desired image coordinates and reconstructed attitude and depth ratio information which guarantees that i the desired equilibrium point is an almost global attractor ii a set of necessary conditions for feature visibility holds throughout the system s trajectories and iii the image of a predefined feature point is kept inside the camera s field of view

estimates and structure of α harmonic functions we prove a uniform boundary harnack inequality for nonnegative harmonic functions of the fractional laplacian on arbitrary open set d this yields a unique representation of such functions as integrals against measures on dc satisfying an integrability condition the corresponding martin boundary of d is a subset of the euclidean boundary determined by an integral test

logarithmic control trajectory tracking and formation for nonholonomic vehicles on lie group se 2 abstractthis paper studies the problem of set point stabilisation trajectory tracking and formation tracking for unicycle type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the lie group setting of the special euclidean group se 2 motivated by recent developments in geometric control approaches for holonomic systems we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too we then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the lie algebra preserves the velocity constraint this leads to a global control law which is valid for general time varying as well as non smooth trajectories the tracking control law is also applied to the problem of leader follower formation tracking by constr

robust attitude tracking for rigid spacecraft with prescribed transient performance abstractthis paper investigates the prescribed performance attitude tracking control problem of a rigid spacecraft with uncertain dynamics and bounded disturbances by suitable selection of the configuration error function the trajectory tracking problem on so 3 is transformed into a point stabilisation problem of an error dynamic system in the associated lie algebra the predefined transient performance indexes which include the maximum steady state error and overshoot and the minimum convergence rate of the attitude error vector are characterised as the inequality constraints for the tracking controller design the error transformation technique is utilised to transform the attitude error dynamics with inequality constraints to an equivalent unconstrained error one then a coordinate free robust tracking controller is designed for the unconstrained error dynamics to solve the prescribed performance attitude tracking control problem a rigorous mathematical stability proof is given finally n

the effects of randomizing values of interaural disparities on binaural detection and on discrimination of interaural correlation the purpose of this study was to assess whether randomizing roving baseline interaural parameters of binaural stimuli would adversely affect performance in masking level difference and in interaural correlation discrimination paradigms listeners detection thresholds were measured in noso and nos configurations for both broadband 100 3000 hz and narrow band 450 550 hz maskers centered at 500 hz in addition thresholds of interaural decorrelation from a reference correlation of 1 0 were measured for 100 hz wide bands of noise centered at 500 hz data were obtained under conditions in which either values of itd or values of iid were roved both within and across trials data were also collected in the absence of a rove the range of the rove was 500 s for itds and was 6 db for iids the duration of the stimuli was varied between 17 and 310 ms overall the results indicate that independent of duration roving the interaural cues produced small degradations of performance as compared to data ob

brief freedom in coordinate transformation for exact linearization and its application to transient behavior improvement this paper deals with the use of extra freedom in the exact linearization technique firstly the freedom in choosing the coordinate transformation and nonlinear state feedback for the exact linearization is clarified secondly a controller design strategy for the transient behavior improvement in the presence of impulsive disturbances is shown finally numerical and experimental examples exhibit the effectiveness of this method

controlled lagrangians and the stabilization of mechanical systems ii potential shaping for pt i see ibid vol 45 p 2253 70 2000 we extend the method of controlled lagrangians cl to include potential shaping which achieves complete state space asymptotic stabilization of mechanical systems the cl method deals with mechanical systems with symmetry and provides symmetry preserving kinetic shaping and feedback controlled dissipation for state space stabilization in all but the symmetry variables potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables the approach also extends the method of controlled lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

a geometric approach for quadrotor trajectory tracking control this paper investigates the trajectory tracking problem for quadrotor with attitude finite time convergence via geometric approach first a global geometric dynamic description is presented on the special euclidean group se 3 and the trajectory tracking control is decomposed into two cascaded tracking control loops the position tracking control loop and the attitude tracking control loop then based on the fact that the attitude tracking loop is a fast loop a finite time controller based on the exponential coordinate is proposed to speed up the response rate of the attitude control loop so that the artificial singularity and redundancy can be avoided in addition a backstepping controller is designed for the position tracking loop to construct the thrust magnitude control input for the position dynamics and the reference rotation matrix for the attitude tracking loop finally the numerical simulation results are presented to demonstrate the effectiveness of this trajectory tracking strategy

design of differentially flat planar space robots and their planning and control the motion of free floating space robots is characterized by non holonomic constraints i e non integrable rate constraint equations these constraints originate from the principles of conservation of angular momentum it is well known that these rate constraints can also be written to form an input affine drift less control systems trajectory planning of these systems is extremely challenging and computation intensive since the motion must satisfy differential constraints under certain conditions these drift less control systems can be shown to be differentially flat the property of flatness allows a computationally inexpensive way to plan trajectories for a dynamic system between two configurations as well as develop feedback controllers the key contribution of this paper is to systematically study the non holonomic rate constraints for free floating planar open chain robots and determine the design conditions under which the system exhibits differential flatness a design is then proposed that c

control of underactuated spacecraft with bounded inputs bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft the flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem

intrinsic observer based stabilization for simple mechanical systems on lie groups this paper presents a dynamic observer for a class of simple mechanical systems on lie groups this observer provides velocity estimates based on configuration measurements the observer is textit intrinsic so its performance does not depend on the choice of coordinates and it is textit coordinate free in the sense that the equations may be written explicitly without specifying coordinates for the configuration space our main result is obtained by specializing a previous result of aghannan and rouchon concerning velocity estimation of simple mechanical systems on riemannian manifolds to such systems on lie groups this specialization is nonobvious and extremely powerful further we extend the original result to include velocity dependent external forces this estimator combined with a coordinate free formulation of passivity based state feedback control allows the construction of a coordinate free intrinsic dynamic output feedback compensator this is to our knowledge the first time such a result has been reported explicit expressions are computed for the lie groups so 3 and se 3 allowing easy specialization to practical problems of rigid body motion the theory is illustrated via application to the axisymmetric top and to a six degrees of freedom microelectromechanical system

constructive controllability algorithms for motion planning and optimization presents algorithms for planning feasible and minimum energy paths the algorithms rely on series expansions to characterize planning problems for polynomial control systems the resulting inversion problem is solved through an iterative contraction or a power series inversion while the design methodology is general our focus is on a class of polynomial control systems for which we provide explicit convergence guarantees we demonstrate performance and numerical characteristics using one dimensional and six dimensional systems

regularity theory for general stable operators abstract we establish sharp regularity estimates for solutions to l u f in r n l being the generator of any stable and symmetric levy process such nonlocal operators l depend on a finite measure on s n 1 called the spectral measure first we study the interior regularity of solutions to l u f in b 1 we prove that if f is c then u belong to c 2 s whenever 2 s is not an integer in case f l we show that the solution u is c 2 s when s 1 2 and c 2 s for all 0 when s 1 2 then we study the boundary regularity of solutions to l u f in u 0 in r n in c 1 1 domains we show that solutions u satisfy u d s c s for all 0 where d is the distance to finally we show that our results are sharp by constructing two counterexamples

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

two sided heat kernel estimates for censored stable like processes in this paper we study the precise behavior of the transition density func tions of censored resurrected stable like processes in c 1 1 open sets in r d where d 1 and 1 2 we first show that the semigroup of the censored stable like process in any bounded lipschitz open set is intrinsically ultracontractive we then establish sharp two sided estimates for the transition density functions of a large class of censored stable like processes in c 1 1 open sets we further obtain sharp two sided estimates for the green functions of these censored stable like processes in bounded c 1 1 open sets

transition probabilities for symmetric jump processes we consider symmetric markov chains on the integer lattice in d dimensions where a 0 2 and the conductance between x and y is comparable to x y d we establish upper and lower bounds for the transition probabilities that are sharp up to constants

configuration flatness of lagrangian systems underactuated by one control lagrangian control systems that are differentially flat with flat outputs that depend only on configuration variables are said to be configuration flat we provide a complete characterization of configuration flatness for systems with n degrees of freedom and n 1 controls whose range of control forces only depends on configuration and whose lagrangian has the form of kinetic energy minus potential the method presented allows us to determine if such a system is configuration flat and if so provides a constructive method for finding all possible configuration flat outputs our characterization relates configuration flatness to riemannian geometry we illustrate the method with two examples

schauder estimates for drifted fractional operators in the supercritical case abstract we consider a non local operator l which is the sum of a fractional laplacian 2 0 1 plus a first order term which is measurable in the time variable and locally holder continuous in the space variables importantly the fractional laplacian 2 does not dominate the first order term we show that global parabolic schauder estimates hold even in this case under the natural condition 1 thus the constant appearing in the schauder estimates is in fact independent of the l norm of the first order term in our approach we do not use the so called extension property and we can replace 2 with other operators of stable type which are somehow close including the relativistic stable operator moreover when 1 2 1 we can prove schauder estimates for more general stable type operators like the singular cylindrical one i e when 2 is replaced by a sum of one dimensional fractional laplacians k 1 d x k x k 2 2

boundary regularity for fully nonlinear integro differential equations we study fine boundary regularity properties of solutions to fully nonlinear elliptic integro differential equations of order 2s with s 0 1 we consider the class of nonlocal operators l l 0 which consists of all the infinitesimal generators of stable levy processes belonging to the class l0 of caffarelli silvestre for fully nonlinear operators i elliptic with respec tt ol w e prove that solutions to iu f in u 0 in r n satisfy u d s c s for all 0 where d is the distance to a ndf l we expect the holder exponent s to be optimal or almost optimal for general right hand sides f l moreover we also expect the class l to be the largest scale invariant subclass of l0 for which this result is true in this direction we show that the class l0 is too large for all solutions to behave like d s the constants in all the estimates in this paper remain bounded as th eo rder of the equation approaches 2

simple mechanical control systems with constraints we apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints certain simple aspects of the theory of affine connections play an important part in our presentation the necessary background is presented in order to illustrate how the methods may be applied the bulk of this paper is devoted to a detailed analysis of some examples of nonholonomic mechanical control systems we look at the heisenberg system the upright rolling disk the roller racer and the snakeboard

binaural detection with narrowband and wideband reproducible noise maskers iv models using interaural time level and envelope differences the addition of out of phase tones to in phase noises results in dynamic interaural level difference ild and interaural time difference itd cues for the dichotic tone in noise detection task several models have been used to predict listeners detection performance based on ild itd or different combinations of the two cues the models can be tested using detection performance from an ensemble of reproducible noise maskers previous models cannot predict listeners detection performance for reproducible noise maskers without fitting the data here two models were tested for narrowband and wideband reproducible noise experiments one model was a linear combination of ild and itd that included the generally ignored correlation between the two cues the other model was based on a newly proposed cue the slope of the interaural envelope difference sied predictions from both models explained a significant portion of listeners performance for detection of a 500 hz tone in wideband noise predictions based on the sied approached the predictable variance in the wideband condition the sied represented a nonlinear combination of ild and itd with the latter cue dominating listeners did not use a common strategy cue to detect tones in the narrowband condition and may use different single frequencies or different combinations of frequency channels

invariant feedback control for the kinematic car on the sphere abstract the design of an invariant tracking control law for the kinematic car driving on a sphere is discussed using a lie group framework a left invariant description on so 3 is derived basic geometric considerations allow a direct comparison of the model with the planar case using a geometrically motivated invariant tracking error on s 2 an invariant feedback design is proposed finally one possible design of an invariant asymptotic observer is sketched

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

stabilization of relative equilibria for underactuated systems on riemannian manifolds steady motions of mechanical systems with symmetry are stabilized via a potential shaping and damping control a general methodology based on riemannian geometry tools provides exponential stabilization over the full phase space

finite time stable tracking control for an underactuated system in se 3 in discrete time we consider tracking control of an underactuated system on the tangent bundle of the six dimensional lie group of rigid body motions s e 3 we formulate a finite time stable fts tracking co

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

configuration controllability of mechanical systems underactuated by one control we investigate local configuration controllability for mechanical control systems within the affine connection formalism we rely on previous results on controllability and series expansions for the evolution of mechanical systems starting from rest extending the work by lewis for the single input case we are able to characterize local configuration controllability for systems with n degrees of freedom and n 1 input forces

harnack inequalities for non local operators of variable order we consider harmonic functions with respect to the operator formula math under suitable conditions on n x h we establish a harnack inequality for functions that are nonnegative and harmonic in a domain the operator l is allowed to be anisotropic and of variable order

harnack inequality for some classes of markov processes in this paper we establish a harnack inequality for nonnegative harmonic functions of some classes of markov processes with jumps

non local dirichlet forms and symmetric jump processes we consider the non local symmetric dirichlet form e f given by with f the closure with respect to e 1 of the set of c 1 functions on r d with compact support where e 1 f f e f f f rd f x 2 dx and where the jump kernel j satisfies for 0 2 x y 1 this assumption allows the corresponding jump process to have jump intensities whose sizes depend on the position of the process and the direction of the jump we prove upper and lower estimates on the heat kernel we construct a strong markov process corresponding to e f we prove a parabolic harnack inequality for non negative functions that solve the heat equation with respect to e finally we construct an example where the corresponding harmonic functions need not be continuous

heat kernel estimates for jump processes of mixed types on metric measure spaces in this paper we investigate symmetric jump type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces the class of metric measure spaces includes the alfors d regular sets which is a class of fractal sets that contains geometrically self similar sets a typical example of our jump type processes is the symmetric jump process with jumping intensity e c 0 x y x y int alpha 1 alpha 2 frac c alpha x y x y d alpha nu d alpha where is a probability measure on alpha 1 alpha 2 subset 0 2 c x y is a jointly measurable function that is symmetric in x y and is bounded between two positive constants and c 0 x y is a jointly measurable function that is symmetric in x y and is bounded between 1 and 2 where either 2 1 0 or 1 2 0 this example contains mixed symmetric stable processes on mathbb r n as well as mixed relativistic symmetric stable processes on mathbb r n we establish parabolic harnack principle and derive sharp two sided heat kernel estimate for such jump type processes

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object that we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

coordinate independent adaptive attitude tracking control design for spacecraft robust to time varying system uncertainties abstractin this paper we consider the adaptive attitude control of spacecraft with time varying inertial properties we use a coordinate independent approach for the purpose of designing the control and estimation laws in terms of the rotation matrices representing the spacecraft body frame and reference tracking signals this method helps to overcome the difficulties regarding the attitude representation on so 3 such as ambiguities associated with quaternion representation and inherent singularities inside euler parameters we model the time variations in inertial parameters in two different ways and design adaptive control schemes for each case as the first uncertain dynamic model we consider a setting of spacecraft with multiple moving appendages and based on this model design an adaptive control scheme with three different versions where frobenious norm is used in measuring the deviation of the estimated inertia tensors from their actual values the proposed adaptive control scheme is later ex

regularity results for stable like operators for 1 2 we consider operators of the form lf x rd f x h f x 1 h 1 f x h a x h h d dh and for 0 1 we consider the same operator but where the f term is omitted we prove under appropriate conditions on a x h that any solution u to lu f will be in c if f c

controllability and motion algorithms for underactuated lagrangian systems on lie groups we provide controllability tests and motion control algorithms for underactuated mechanical control systems on lie groups with lagrangian equal to kinetic energy examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space local controllability properties of these systems are characterized and two algebraic tests are derived in terms of the symmetric product and the lie bracket of the input vector fields perturbation theory is applied to compute approximate solutions for the system under small amplitude forcing in phase signals play a crucial role in achieving motion along symmetric product directions motion control algorithms are then designed to solve problems of point to point reconfiguration static interpolation and exponential stabilization we illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies satellites and underwater vehicles

abstractions of hamiltonian control systems given a control system and a desired property an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail in previous work abstractions of linear and nonlinear control systems were considered while preserving reachability properties in this paper we consider the abstraction problem for hamiltonian control systems where in addition to the property of interest we also preserve the hamiltonian structure of the control system we show how the hamiltonian structure of control systems can be exploited to simplify the abstraction process we then focus on local accessibility preserving abstractions and provide conditions under which local accessibility properties of the abstracted hamiltonian system are equivalent to the local accessibility properties of the original hamiltonian control system

rotational motion control of a spacecraft this note describes a systematic procedure for the control synthesis of a rigid spacecraft using the energy shaping method the geometric concept of a mechanical system in a coordinate independent form is used to derive a control algorithm for the euler poincare equations the main result of this note is a specialization of the method on the unit quaternion group this note is concluded with the examples of the potential functions and implementation for the three axis attitude control problem

almost global tracking of simple mechanical systems on a general class of lie groups we present a general intrinsic tracking controller design for fully actuated simple mechanical systems when the configuration space is one of a general class of lie groups we first express a state feedback controller in terms of a function the error function satisfying certain regularity conditions if an error function can be found then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition with locally exponential convergence asymptotic convergence from almost every initial condition is referred to as almost global asymptotic stability error functions may be shown to exist on any compact lie group or any lie group diffeomorphic to the product of a compact lie group and r sup n this covers many cases of practical interest such as so n se n their subgroups and direct products we show here that for compact lie groups the dynamic configuration feedback controller obtained by composing the full state feedback law with an exponentially convergent velocity observer is also almost globally asymptotically stable with respect to the tracking error we emphasize that no invariance is needed for these results however for the special case where the kinetic energy is left invariant we show that the explicit expression of these controllers does not require coordinates on the lie group the controller constructions are demonstrated on so 3 and simulated for the axi symmetric top results show excellent performance

robust point stabilization of underactuated mechanical systems via the extended chained form this paper addresses point stabilization for the extended chained form ecf a control system that may be used to model a number of mechanical underactuated systems a control law is proposed based on well known hybrid open loop feedback techniques which exponentially stabilizes the origin of a dynamic extension of the ecf and ensures a degree of robustness to additive disturbance terms that may represent for instance model uncertainties numerical simulations are included to illustrate the performance of the presented stabilizers

brief steering of a class of nonholonomic systems with drift terms in the present paper nonholonomic systems with drift terms are studied the discussion is focused on a class of lagrangian systems with a cyclic coordinate we present an approach to open loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs a control procedure is derived and it is applied to the planar diver

further passivity results for the attitude control problem in this paper we establish passivity for the system which describes the attitude motion of a rigid body in terms of minimal three dimensional kinematic parameters in particular we show that linear asymptotically stabilizing controllers and control laws without angular velocity measurements follow naturally from these passivity properties the results of this paper extend similar results for the case of the nonminimal euler parameters

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

on almost global tracking for a certain class of simple mechanical systems in this paper we propose a control law for the almost global asymptotic tracking agat of a smooth reference trajectory for a fully actuated simple mechanical system sms evolving on a riemannian manifold that can be embedded in a euclidean space the existing results on tracking for an sms are either local or almost global only in the case the manifold is a lie group in the latter case the notion of a configuration error is naturally defined by the group operation and facilitates a global analysis however such a notion is not intrinsic to a riemannian manifold in this paper we define a configuration error followed by error dynamics on a riemannian manifold and then prove the agat the results are demonstrated for a spherical pendulum which is an sms on s 2 and for a particle moving on a lissajous curve in mathbb r 3

passivity based adaptive attitude control of a rigid spacecraft an adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion the tracking error is described with the euler parameter vector global convergence of the tracking error to zero is shown using passivity theory this allows for the use of time varying positive definite feedback gain matrices and the results can easily be extended to other passive parameter update laws

passive decomposition of mechanical systems with coordination requirement we show the fundamental passive decomposition property of general mechanical systems on a n dim configuration manifold m i e when endowed with a submersion h m n where n is a m dim manifold m n their lagrangian dynamics with the kinetic energy as the lagrangian can always be decomposed into 1 shape system describing the m dim dynamics of h q on n 2 locked system representing the n m dim dynamics along the level set of h and 3 energetically conservative coupling between them the locked and shape systems also individually inherit the lagrangian structure and passivity of the original dynamics we exhibit and analyze geometric and energetic properties of the passive decomposition in a coordinate free manner an illustrative example on so 3 is also provided

the geometric convexity on se 3 and its application to the formation tracking in multi vehicle systems abstractthis paper considers the problem of geometric convexity on special euclidean group se 3 and its application to the formation tracking in multi vehicle systems motivated by the convex hull on euclidean space the specific expression of geodesic connecting two points on se 3 is obtained based on the pontryagin s minimum principle then it is extended to the geometric convex combination for multiple points based on which the virtual systems on se 3 is given to be used in the application of formation tracking problem in light of the geometric convex combination and virtual systems on se 3 a consensus based tracking protocol is proposed to guarantee that the formation is achieved under the directed acyclic graphs finally two numerical examples are provided to demonstrate the validity of the theoretical results

binaural processing model based on contralateral inhibition iii dependence on temporal parameters this paper and two accompanying papers breebaart et al j acoust soc am 110 1074 1088 2001 110 1089 1104 2001 describe a computational model for the signal processing of the binaural auditory system the model consists of several stages of monaural and binaural preprocessing combined with an optimal detector simulations of binaural masking experiments were performed as a function of temporal stimulus parameters and compared to psychophysical data adapted from literature for this purpose the model was used as an artificial observer in a three interval forced choice procedure all model parameters were kept constant for all simulations model predictions were obtained as a function of the interaural correlation of a masking noise and as a function of both masker and signal duration furthermore maskers with a time varying interaural correlation were used predictions were also obtained for stimuli with time varying interaural time or intensity differences finally binaural forward maskin

an intrinsic pid controller for mechanical systems on lie groups this paper shows how integral action may be implemented intrinsically in the general setting of fully actuated mechanical systems on lie groups when combined with an intrinsic formulation of pd control integral action ensures that a suitably defined configuration tracking error will converge to zero in response to constant velocity commands and disturbance forces convergence is locally exponential and almost global and is robust to bounded parametric uncertainty for more general bounded commands and disturbances the tracking error can be made arbitrarily small by choosing sufficiently large controller gains a separation principle allows the addition of an intrinsic velocity observer to complete a geometric analog to the familiar output feedback pid controller for second order linear systems the controller extends naturally to accommodate tracking of equivariant output functions the result is explicitly shown for the lie group so 3 and supported by simulations of a 6dof quadrotor model

nonlinear control of mechanical systems with an unactuated cyclic variable numerous robotic tasks associated with underactuation have been studied in the literature for a large number of these in the plane the mechanical models have a cyclic variable the cyclic variable is unactuated and all shape variables are independently actuated this paper formulates and solves two control problems for this class of models if the generalized momentum conjugate to the cyclic variable is not conserved conditions are found for the existence of a set of outputs that yields a system with a one dimensional exponentially stable zero dynamics i e an exponentially minimum phase system along with a dynamic extension that renders the system locally input output decouplable if the generalized momentum conjugate to the cyclic variable is conserved a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics along with a dynamic extension that renders the system feedback linearizable a common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components the function arises by partially integrating the conjugate momentum the results are illustrated on two balancing tasks and on a ballistic flip motion

symmetric stable laws and stable like jump diffusions asymptotic expansions are obtained for finite dimensional symmetric stable distributions they are used to prove the existence of continuous transition probability densities of stable and stable like jump diffusions and to construct local multiplicative asymptotics and global two sided estimates for these densities as a consequence the distribution of the first passage times for stable jump diffusions is estimated and the integral test for the limsup behaviour of their sample paths as t to 0 is provided 1991 mathematics subject classification 60e07 60g17 60j35 47d07

uniqueness in law for pure jump markov processes let a be the operator defined on c2 functions by af left x right smallint left f left x h right f left x right f left x right h 1 1 1 left h right right v left x dh right sufficient conditions are given for existence and uniqueness for the martingale problem associated with a in the case of stable like processes where v x dh is equal to the levy measure for the stable symmetric process of index x for each x the conditions reduce to x continuous for existence and x dini continuous for uniqueness

stabilization of a 3d axially symmetric pendulum stabilizing controllers are developed for a 3d pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry this assumption allows development of a reduced model that forms the basis for controller design and global closed loop analysis this reduced model is parameterized by the constant angular velocity component of the 3d pendulum about its axis of symmetry several different controllers are proposed controllers based on angular velocity feedback only asymptotically stabilize the hanging equilibrium then controllers are introduced based on angular velocity and reduced attitude feedback that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium these problems can be viewed as stabilization of a lagrange top finally if the angular velocity about the axis of symmetry is assumed to be zero controllers are introduced based on angular velocity and reduced attitude feedback that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium this problem can be viewed as stabilization of a spherical pendulum

boundary regularity for nonlocal operators with kernels of variable orders abstract we study the boundary regularity of solutions of the dirichlet problem for the nonlocal operator with a kernel of variable orders since the order of differentiability of the kernel is not represented by a single number we consider the generalized holder space we prove that there exists a unique viscosity solution of l u f in d u 0 in r n d where d is a bounded c 1 1 open set and that the solution u satisfies u c v d and u v d d c d with the uniform estimates where v is the renewal function and d d x dist x d

on the computation of π flat outputs for linear time varying differential delay systems abstract we introduce a new definition of flatness for linear differential delay systems with time varying coefficients we characterize and 0 flat outputs and provide an algorithm to efficiently compute such outputs we present an academic example of motion planning to discuss the pertinence of the approach

asymptotic smooth stabilization of the inverted 3 d pendulum the 3 d pendulum consists of a rigid body supported at a fixed pivot with three rotational degrees of freedom it is acted on by gravity and it is fully actuated by control forces the 3 d pendulum has two disjoint equilibrium manifolds namely a hanging equilibrium manifold and an inverted equilibrium manifold the contribution of this paper is that two fundamental stabilization problems for the inverted 3 d pendulum are posed and solved the first problem asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and attitude of the 3 d pendulum the second problem asymptotic stabilization of the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3 d pendulum these control problems for the 3 d pendulum exemplify attitude stabilization problems on the configuration manifold so 3 in the presence of potential forces lyapunov analysis and nonlinear geometric methods are used to assess global closed loop properties yielding a characterization of the almost global domain of attraction for each case

nonholonomic control systems on riemannian manifolds this paper gives a general formulation of the theory of nonholonomic control systems on a riemannian manifold modeled by second order differential equations and using the unique riemannian connection defined by the metric the main concern is to introduce a reduction scheme replacing some of the second order equations by first order equations the authors show how constants of motion together with the nonholonomic constraints may be combined to yield such a reduction the theory is applied to a particular class of nonholonomic control systems that may be thought of as modeling a generalized rolling ball this class reduces to the classical example of a ball rolling without slipping on a horizontal plane

on the topological structure of attraction basins for differential inclusions abstract we show that when a compact set is globally asymptotically stable under the action of a differential inclusion satisfying certain regularity properties there exists a smooth differential equation rendering the same compact set globally asymptotically stable the regularity properties assumed in this work stem from the consideration of krasovskii filippov solutions to discontinuous differential equations and the robustness of asymptotic stability under perturbation in particular the results in this work show that when a compact set cannot be globally asymptotically stabilized by continuous feedback due to topological obstructions it cannot be robustly globally asymptotically stabilized by discontinuous feedback either the results follow from converse lyapunov theory and parallel what is known for the local stabilization problem

brief paper the spring paradigm in tracking control of simple mechanical systems an intrinsic formulation of geometric proportional derivative tracking control for fully actuated mechanical systems is developed the region of stability is determined directly from the size of the system s injectivity radius and for a restricted set of control problems the system s locus of cut points about a desired reference point exponential stability is obtained under certain boundedness conditions for controlled motion along a geodesic the proffered scheme yields a particularly simple and elegant manifestation of the underlying use of the mass spring damper paradigm in the control design methodology

new class of control laws for robotic manipulators part 1 non adaptive case a new class of exponentially stabilizing control laws for joint level control of robot arms is introduced it has recently been recognized that the non linear dynamics associated with robotic manip

global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced attitude tracking for rigid bodies in this paper we propose a hybrid feedback based on a synergistic potential function that achieves global asymptotic stabilization of a desired orientation on the n sphere with a nominal robustness to measurement disturbances a task that is not possible by classical feedback be it smooth nonsmooth periodic or any combination thereof due to the topological structure of the sphere we extend this basic result to a tracking controller for the reduced attitude or pointing direction of a rigid body and provide a method to remove jumps in the controlled torque by backstepping the proposed hybrid feedback is compared with a similar smooth feedback in simulation where it is illustrated that the hybrid feedback overcomes performance limitations inherent to the smooth feedback we provide two examples of a synergistic potential function one defined on a general sphere and the other on the unit circle

accounting for binaural detection as a function of masker interaural correlation effects of center frequency and bandwidth binaural detection was measured as a function of the center frequency bandwidth and interaural correlation of masking noise thresholds were obtained for 500 hz or 125 hz s tonal signals and for the latter stimuli noise or signal plus noise transposed to 4 khz a primary goal was assessment of the generality of van der heijden and trahiotis j acoust soc am 101 1019 1022 1997 hypothesis that thresholds could be accounted for by the additive masking effects of the underlying no and n components of a masker having an interaural correlation of results indicated that 1 the overall patterning of the data depended neither upon center frequency nor whether information was conveyed via the waveform or by its envelope 2 thresholds for transposed stimuli improved relative to their low frequency counterparts as bandwidth of the masker was increased 3 the additivity approach accounted well for the data across stimulus conditions but consistently overestimated mlds especially for narrowband maskers 4 a quantitative approach explicitly taking into account the distributions of time varying itd based lateral positions produced by masker alone and signal plus masker waveforms proved more successful albeit while employing a larger set of assumptions parameters and computational complexity

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

regularity theory for the fractional harmonic oscillator abstract in this paper we develop the theory of schauder estimates for the fractional harmonic oscillator h x 2 0 1 more precisely a new class of smooth functions c h k is defined in which we study the action of h in fact these spaces are those adapted to the operator h hence the suited ones for this type of regularity estimates in order to prove our results an analysis of the interaction of the hermite riesz transforms with the holder spaces c h k is needed that we believe of independent interest

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

the contribution of static and dynamically varying itds and iids to binaural detection this paper investigates the relative contribution of various interaural cues to binaural unmasking in conditions with an interaurally in phase masker and an out of phase signal mos pi by using a modified version of multiplied noise as the masker and a sinusoid as the signal conditions with only interaural intensity differences iids only interaural time differences itds or combinations of the two were realized in addition the experimental procedure allowed the presentation of specific combinations of static and dynamically varying interaural differences in these conditions with multiplied noise as masker the interaural differences have a bimodal distribution with a minimum at zero iid or itd additionally by using the sinusoid as masker and the multiplied noise as signal a unimodal distribution of the interaural differences was realized through this variation in the shape of the distributions the close correspondence between the change in the interaural cross correlation and the size of the interaural differences is no longer found in contrast to the situation for a gaussian noise masker domnitz and colburn j acoust soc am 59 598 601 1976 when analyzing the mean thresholds across subjects the experimental results could not be predicted from parameters of the distributions of the interaural differences the mean the standard deviation or the root mean square value a better description of the subjects performance was given by the change in the interaural correlation but this measure failed in conditions which produced a static interaural intensity difference the data could best be described by using the energy of the difference signal as the decision variable an approach similar to that of the equalization and cancellation model

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object which we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

censored stable processes we present several constructions of a censored stable process in an open set d rn i e a symmetric stable process which is not allowed to jump outside d we address the question of whether the process will approach the boundary of d in a finite time we give sharp conditions for such approach in terms of the stability index and the thickness of the boundary as a corollary new results are obtained concerning besov spaces on non smooth domains including the critical exponent case we also study the decay rate of the corresponding harmonic functions which vanish on a part of the boundary we derive a boundary harnack principle in c1 1 open sets

probability distributions of interaural phase and level differences in binaural detection stimuli probability distributions of interaural phase and level differences are derived for the stimuli used in many studies of binaural detection and interaural correlation discrimination example distributions are shown and summary plots give the standard deviations of these distributions as functions of signal to noise ratio