achieving minimum length scale in topology optimization using nodal design variables and projection functions a methodology for imposing a minimum length scale on structural members in discretized topology optimization problems is described nodal variables are implemented as the design variables and are projected onto element space to determine the element volume fractions that traditionally define topology the projection is made via mesh independent functions that are based upon the minimum length scale a simple linear projection scheme and a non linear scheme using a regularized heaviside step function to achieve nearly 0 1 solutions are examined the new approach is demonstrated on the minimum compliance problem and the popular simp method is used to penalize the stiffness of intermediate volume fraction elements solutions are shown to meet user defined length scale criterion without additional constraints penalty functions or sensitivity filters no instances of mesh dependence or checkerboard patterns have been observed copyright 2004 john wiley sons ltd

controllability and stability analysis of planar snake robot locomotion this paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics the paper has five contributions 1 a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed 2 a stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time varying 3 a controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic the analysis also shows that the snake robot does not satisfy sufficient conditions for small time local controllability stlc 4 an analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface the explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion 5 a controller for straight line path following control of snake robots is proposed and a poincare map is investigated to prove that the resulting state variables of the snake robot except for the position in the forward direction trace out an exponentially stable periodic orbit

topology optimization with pressure load through a level set method abstract the topology optimization problem with pressure load is solved by using a level set method the free boundary and the pressure boundary of a structure are represented separately as two zero level sets of two level set functions and they are independently propagated during the optimization by solving two hamilton jacobi equations in order to prevent the two boundaries from touching or crossing each other the design velocities of the two boundaries that amount to the steepest descent directions are modified the optimization problem of minimum compliance with perimeter regularization is considered the shape derivatives of the two boundaries are derived by using the material derivative approach and the adjoint method the finite element analysis is done through an eulerian method by employing a fixed mesh and an artificial weak material that represents void numerical examples in two dimensions are investigated

minimum length scale control in structural topology optimization based on the moving morphable components mmc approach abstract a novel approach which can control the minimum length scale in topology optimization in a straightforward and explicit way is proposed in the present paper this approach is constructed under the so called moving morphable components mmc based solution framework where optimized structural topology can be found by changing the shapes and layout of a set of trapezoid shaped structural components on a fixed finite element mesh the extended finite element method xfem is employed for structural response analysis and shape sensitivity information is obtained by carrying out numerical integration along the structural boundary a precision definition of the minimum length scale of a structure is also suggested based on the proposed solution framework compared with existing approaches the proposed approach can achieve minimum length scale control by simply setting lower bounds on a set of geometric design variables only a small number of purely geometric constraints imposed on the sizes of intersection regions should be considered explicitly in order to get a complete minimum length scale control numerical examples demonstrate the effectiveness of the proposed method

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

an investigation concerning optimal design of solid elastic plates abstract we consider the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory assuming the material volume and plate domain to be given we use the plate thickness function as the design variable and take both maximum and minimum allowable thickness values into account on the basis of a convenient tensorial formulation of the problem where the governing equations are derived by variational analysis and constitute necessary conditions for stationarity we develop an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained these numerical results enable us to investigate the optimization problem itself in terms of its major parameters particularly the maximum and minimum values specified for the plate thickness for problems associated with large ratios between these constraint values plate designs with significant integral stiffeners are obtained we find however that these designs are only local optima and that a global optimal plate thickness function does generally neither exist within the class of smooth functions nor within the class of smooth functions with a finite number of discontinuities in order to determine a global optimal solution associated with given thickness constraint values it is therefore necessary to change the optimal design formulation with implications for a number of similar two dimensional optimization problems our results offer valuable indications of the lines along which such changes should be performed

explicit layout control in optimal design of structural systems with multiple embedding components in this paper two novel methods are proposed for optimizing the layout of structural systems with embedding components considering the minimum maximum distance constraints between the components the key ideas are using level set functions to describe the shapes of arbitrary irregular embedding components and resorting to the concept of structural skeleton to formulate the distance control constraints explicitly numerical examples presented demonstrate that the proposed approaches can give a complete control of the layout of embedding components in an explicit and local way

topology optimization with multiple phase projection topology optimization is a powerful tool capable of generating new solutions to engineering design problems while these designs may offer optimal performance in a computational setting it is not uncommon for them to be impractical or unrealizable from engineering or fabrication points of view this challenge motivates the present work a methodology is proposed for restricting the minimum length scale of each material phase used in the design the technique allows a designer to for example prescribe a minimum allowable length scale of structural members solid phase as well as the minimum allowable length scale on holes void phase the proposed approach utilizes the heaviside projection method hpm to continuum topology optimization each material phase is associated with a design variable field that is projected onto element space using regularized heaviside functions the fields are independently projected and the resulting distributions are assembled to yield topology the technique is demonstrated on classic topology optimization problems including minimum compliance heat conduction and compliant mechanisms solutions are shown to be near discrete topologies satisfying minimum length scale criterion placed on each phase control over length scale is achieved implicitly and therefore the technique does not require additional constraints

topology optimization using moving morphable bars for versatile thickness control abstract topology optimization for minimum and maximum thickness control uniform thickness control and multiple thickness control is provided by using moving morphable bars formed of rectangles with semicircular ends by employing the center coordinates of the semicircular ends and the thickness of a moving bar as design variables the bar can float around the design domain while its shape morphs according to the design sensitivities the overlapping of moving bars is allowed and the element density is determined by the approximation of the heaviside function by measuring the shortest distance from the boundaries of the bars the minimum thickness of the members of an optimized structure is controlled by simply setting the lower bound of the thickness variables for the moving bars no constraints or filtering techniques are required for the minimum thickness control the maximum thickness is controlled for each moving bar through its corresponding constraint which prevents an over sized member due to the overlapping of moving bars by solving benchmark problems the validity of the method proposed for versatile thickness control is shown it is also shown that the proposed method alleviates numerical difficulties for hinges when it is applied for compliant mechanism problems

on the analysis of nonlinear nilpotent switched systems using the hall sussmann system abstract we consider an open problem on the stability of nonlinear nilpotent switched systems posed by daniel liberzon partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems the global structure is crucial in establishing stability we show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system the nilpotent hall sussmann system furthermore local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems we derive several new results revealing the elegant lie algebraic structure of the nilpotent hall sussmann system

topology optimization using regularized intermediate density control abstract we consider topology optimization of elastic continua the elasticity tensor is assumed to depend linearly on the design function density as in the variable thickness sheet problem in order to get black white design pictures the intermediate density values are controlled by an explicit constraint this constraint is regularized by including a compact and linear operator s to guarantee existence of solutions a proof of convergence of the finite element fe discretized optimization problem s solutions to exact ones is also given so the method is not prone to numerical anomalies such as mesh dependence or checkerboards the procedure is illustrated in some minimum compliance examples where s is chosen to be a classical convolution type operator the fe discretized optimization problems are solved by sequential convex approximations

moving morphable patches for three dimensional topology optimization with thickness control abstract thickness controllable topology optimization is presented for three dimensional problems using moving morphable patches geometric features of triangular patches were employed as design variables to enable the representation of shell like members and beam or bar members with a small number of design components the minimum thickness for mean compliance minimization problems can be controlled simply by setting the lower bound of thickness variables of the patches as the given minimum regarding the maximum thickness the patches with close to maximum thicknesses were controlled to be connected on their sides or perfectly overlapped for which a void mask is introduced on each patch avoiding partial overlapping through their faces thus the maximum thickness of a member was obtained as the maximum value of thickness variables of the patches consisting of the member therefore the maximum thickness of members can be controlled by the upper bound of thickness variables a constraint was imposed on the material volume of each patch to prevent partial overlapping or incomplete connection with other patches the effectiveness of the proposed formulation was verified by showing various examples with minimum maximum and uniform thickness controls

some convergence results in perimeter controlled topology optimization abstract the computation of optimal topologies of elastic continuum structures using a constraint on the perimeter is investigated predicting macroscopic black white topologies without the use of homogenization techniques this approach is presently one of the most attractive approaches in topology optimization mathematical justifications are given for both the relaxation of the discrete value constraint on the design variable and for the finite element discretizations it turns out that the way in which the perimeter has been calculated to date the numerical results will not approximate the intended original problem but one with a taxi cab perimeter which measures lengths of structural edges after projection onto the coordinate axes

on the positive output controllability of linear time invariant systems this paper considers the output controllability of autonomous linear control systems that are subject to non negative input constraints based on the evaluation of the geometric properties of the system necessary and sufficient conditions are proposed for the positive output controllability of continuous linear time invariant systems to aid in the practical evaluation of positive output controllability additional sufficient conditions are derived for which efficient numerical techniques exist these conditions are evaluated over a set of numerical examples which support the theoretical results

shape optimization with a level set based mesh evolution method in this article we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process by means of a mesh amenable for mechanical analyses while retaining the whole versatility of the level set method when it comes to accounting for their evolution the key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one and conversely this notably brings into play an algorithm for generating the signed distance function to an arbitrary discrete domain and a mesh generation algorithm for implicitly defined geometries

multi resolution multi scale topology optimization a new paradigm abstract the purpose of this work is to present a new concept multi resolution multi scale topology optimization the key idea of the present strategy is that design optimization should be performed progressively from low to high resolution not at a single resolution level to achieve the multi resolution strategy design optimization is formulated in a wavelet based variable space not in a direct density variable space the major advantages of the multi resolution design optimization include 1 topologically simple and close to the global optimum structures may be obtained without any explicit constraint and 2 the convergence is not sensitive to mathematical programming methods for the efficient numerical implementation of the multi resolution approach the side constraints imposed on the direct density variables are removed by mapping the density variables into intermediate variables these intermediate variables are then wavelet transformed to new design variables it is addressed that the present multi resolution topology optimization can resolve major numerical instability problems such as mesh dependencies and local minima the usefulness of the multi scale nature of the wavelets in the present multi resolution multi scale optimization formulation is also discussed

explicit feature control in structural topology optimization via level set method abstract the present paper aims to address a long standing and challenging problem in structural topology optimization explicit feature control of the optimal topology the basic idea is to resort to the level set solution framework and impose constraints on the extreme values of the signed distance level set function used for describing the topology of the structure numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

exponential stabilization of an underactuated autonomous surface vessel this paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters it is first shown that although the system is not asymptotically stabilizable to a given configuration using a time invariant continuous feedback it is strongly accessible and small time locally controllable at any equilibrium time invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates a simulation example is included to demonstrate the results

optimizing the layout of discrete objects in structures and materials a projection based topology optimization approach abstract this paper uses topology optimization to optimize the layout of discrete objects such as fixed shape void stiffening or functional inclusions in structures and periodic materials the methodology follows a material distribution approach and the heaviside projection method hpm is manipulated to ensure that the designed objects are discrete of fixed size length scale and shape and satisfy minimum spacing requirements these restrictions are achieved implicitly through projection without additional constraints or heuristics the methodology is built in the spirit of free form topology optimization and thus discrete objects are shown to appear vanish or translate across the design domain during the design evolution the technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff circular inclusions

asymptotically stabilizing feedback controls abstract the problem considered is the existence and construction of an asymptotically stabilizing feedback control for a rest solution of an n dimensional single input affine control system the method is to construct high order homogeneous approximations of the vector fields defining the control system which then describe an approximating control system such that an asymptotically stabilizing control of the latter system is a local asymptotically stabilizing control of the original system unlike linear approximations there are many possible nonlinear homogeneous approximations these are constructed from lie algebra filtrations obtained by assigning various weights to the defining vector fields one seeks a weighting hence an approximating system which satisfies the various known necessary conditions for the existence of an asymptotically stabilizing feedback control and for which such a control can be constructed as the solution to a homogeneous hamilton jacobi bellman equation associated with an optimization regulator problem

property β of rolewicz and orthogonal convexities of calderon lozanovskiĭ spaces abstract we find criteria for property of rolewicz and orthogonal convexities in calderon lozanovski spaces in order to present characterization for property in the sequence case we introduce a new respective monotonicity property the particular case of orlicz lorentz spaces will also be discussed

constraints of distance from boundary to skeleton for the control of length scale in level set based structural topology optimization abstract a method is proposed for the control of minimum maximum length scale in the level set based structural topology optimization the minimum maximum length scale of structure is characterized by using the concept of smallest biggest maximal inscribable ball in order to prevent trivial zero minimum length scale the skeleton of structure is utilized and trimmed the control of length scale is realized by constraining the distance from boundary to skeleton and the distance is explicitly constructed by using the highly efficient fast marching method numerical examples in two dimensions are investigated

a new multi material level set topology optimization method with the length scale control capability abstract multi material level set topology optimization methods conventionally rely on the overlap of multiple level set functions to realize the multi material structural representation however this representation may produce redundant material phases and the signed distance information is no longer available within the individual material regions to fix these issues a new multi material level set topology optimization method is proposed in this paper where m level set functions represent m material phases plus the void and the signed distance information is straightforwardly available in each material phase to be specific each level set function corresponds to a material phase and the overlapping areas are filled with an artificial material type the property of which is weaker than any of the involved material types this artificial material plays the role of penalizing the overlap areas to vanish which is different from the close to zero property material type for the void hence the optimization process starts with any multi level set interpolated input and the overlapping areas will gradually vanish based on this new method we have successfully realized the component length scale control on multi material structures and innovatively an approach has been proposed to realize the uniform component thickness control without need of pre specifying the thickness target

further results on the bellman equation for optimal control problems with exit times and nonnegative lagrangians abstract in a series of papers we proved theorems characterizing the value function in exit time optimal control as the unique viscosity solution of the corresponding bellman equation that satisfies appropriate side conditions the results applied to problems which satisfy a positivity condition on the integral of the lagrangian this positive integral condition assigned a positive cost for remaining outside the target on any interval of positive length in this note we prove a new theorem which characterizes the exit time value function as the unique bounded from below viscosity solution of the bellman equation that vanishes on the target the theorem applies to problems satisfying an asymptotic condition on the trajectories including cases where the positive integral condition is not satisfied our results are based on an extended version of barb lat s lemma we apply the theorem to variants of the fuller problem and other examples where the lagrangian is degenerate

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

state steering by learning for a class of nonlinear control systems abstract the problem of steering the state of nonlinearly perturbed linear systems by learning is investigated a family of algorithms which compute the steering control by means of successive trials on the real plant is presented convergence in the face of a class of nonlinear plant perturbations is proven state feedback linearizable systems are shown to be addressable by the presented algorithms two examples illustrate the applicability of algorithms

controllability of linear systems on generalized heisenberg groups this paper is devoted to the study of global controllability of linear systems on higher dimensional heisenberg groups hn necessary conditions and sufficient ones are provided they are compared to the known necessary and sufficient conditions on h1 stated in dath and jouan 2016 controllability of linear systems on low dimensional nilpotent and solvable lie groups journal of dynamical and control systems 22 2 207 225 the notion of decoupled systems is introduced in order to get examples and counter examples and more precise controllability criteria are stated for them

controllability in codimension one abstract local and global controlability of analytic affine control systems with an arbitrary number of controls are studied assuming strong accessibility of and codimension one of the lie algebra t generated by the input vector fields i e dim t p n 1 at every p m controls are assumed to have no a priori bound from the study of the set h where a necessary condition for local controllability at a point is verified and assuming some transversality relations an easy to verify geometric condition is proved h is a submanifold and is locally controllable at every point of h outside a codimension one submanifold a geometric sufficient condition for global controllability on simply connected manifolds is then obtained if every leaf of t intersects the manifold h and some transversality relations including those involved in the local condition are verified is globally controllable

minimum length scale in topology optimization by geometric constraints a density based topology optimization approach is proposed to design structures with strict minimum length scale the idea is based on using a filtering threshold topology optimization scheme and computationally cheap geometric constraints the constraints are defined over the underlying structural geometry represented by the filtered and physical fields satisfying the constraints leads to a design that possesses user specified minimum length scale conventional topology optimization problems can be augmented with the proposed constraints to achieve minimum length scale on the final design no additional finite element analysis is required for the constrained optimization several benchmark examples are presented to show the effectiveness of this approach

a new scheme for imposing a minimum length scale in topology optimization a new scheme for imposing a minimum length scale in topology optimization is presented it guarantees the existence of an optimal design for a large class of topology optimization problems of practical interest it is formulated as one constraint that is computationally cheap and for which sensitivities are also cheap to compute the constraint value is ideally zero but it can be relaxed to a positive value the effect of the method is illustrated in topology optimization for minimum compliance and design of compliant mechanisms notably the method produces compliant mechanisms with distributed flexibility something that has previously been difficult to obtain using topology optimization for the design of compliant mechanisms the term mole method is suggested for the method copyright 2003 john wiley sons ltd

local controllability of scalar input systems on 3 manifolds abstract local controllability of generic c k pairs of vector fields in a three dimensional connected manifold m is studied showing that in general a necessary condition is also sufficient on an open dense subset of the set of points where it is verified the results obtained are used to determine local controllability for scalar input affine control systems

k β and k nearly uniformly convex banach spaces vol 162 no 2 1991 k and k nearly uniformly convex banach spaces denka kutzarova different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of banach spaces in the present paper we introduce other properties of this type namely k and k nearly uniform convexity the definitions as well as some of the results presented here are announced in 7 sullivan 24 has defined k uniformly rotund banach spaces which by a suggestion of davis are all superreflexive fan and glicksberg 1 have introduced fully k convex banach spaces let x1 xk 1 be vectors in a banach space x the k dimensional volume enclosed by x1 xk 1 is given by v x1 x2 xk 1

high order variations for families of vector fields sufficient conditions involving lie brackets of arbitrarily high order are obtained for local controllability of families of vector fields after providing a general framework for the generation of high order control variations we propose a specific method for generating such variations the theory is applied to a number of nontrivial examples

a level set method for shape and topology optimization of both structure and support of continuum structures abstract we present a level set method for the shape and topology optimization of both structure and support two level set functions are used to implicitly represent a structure the traction free boundary and the dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization the optimization problem of minimum compliance is considered the shape derivatives of both boundaries are derived by using a lagrangian function and the adjoint method the finite element analysis is done by modifying a fixed background mesh and we do not use the artificial weak material numerical examples in two dimensions are investigated

explicit control of structural complexity in topology optimization abstract in topology optimization design specific requirements over the complexity of component geometry often need to be satisfied for practical purposes in this paper with the introduction of a novel complexity control measure built on the structural skeletons of solid and void regions an explicit structural complexity control approach for the topology optimization of continuum structures is proposed under the framework of level set representation the use of skeletons enables us to control the minimum sizes of structural holes so as to meet the manufacturing demands through numerical comparison with the cases that have been investigated implicitly we show that the proposed approach is an effective tool to control the structural complexity in an explicit way

local δ2e x condition as a crucial tool for local structure of calderon lozanovskiĭ spaces abstract we shall give a full criterion for a point x e to be a point of order continuity of calderon lozanovski spaces e in order to get that result we introduce the new local 2 e x condition which appears to be necessary and sufficient for this goal next we study the structure of points of lower local uniform monotonicity llum for short we give a result concerning general kothe sequence spaces and we present a characterization for llum points in calderon lozanovski spaces

controllability is harder to decide than accessibility this article compares the difficulties of deciding controllability and accessibility these are standard properties of control systems but complete algebraic characterizations of controllability have proved elusive the article shows in particular that for subsystems of bilinear systems accessibility can be decided in polynomial time but controllability is np hard

geometric conditions for local controllability abstract small time local controllability of a c1 affine control system with a generic drift vector field and n 1 linearly independent input vector fields on an n dimensional connected c1 manifold m is studied showing that a necessary condition namely the drift vector field belonging to the convex hull of the control vector fields at the given point is also sufficient on an open dense subset h1 of the set of points where it is verified local controllability at the points in the interior of h 1 is also considered when the input vector fields generate an involutive distribution and a criterion based on the type of contract of h with the hyperplane spanned by the input vector fields is proved an example shows a situation where the sufficient condition for small time local controllability of h sussmann siam j control option 25 1987 158 194 cannot be applied but in which the method now presented distinguishes the possible cases

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

proximal analysis and the minimal time function under general hypotheses on the target set s and the dynamics of the system we show that the minimal time function ts cdot is a proximal solution to the hamilton jacobi equation uniqueness results are obtained with two different kinds of boundary conditions a new propagation result is proven and as an application we give necessary and sufficient conditions for ts cdot to be lipschitz continuous near s a petrov type modulus condition is also shown to be sufficient for continuity of ts cdot near s

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

local controllability for families of diffeomorphisms abstract we study groups and semigroups which are generated by analytic families of diffeomorphisms the central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold which generalizes the familiar notion of local controllability of control systems with continuous as well as discrete time lie theory methods are used we systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

motion planning for control affine systems satisfying low order controllability conditions abstractthis paper is devoted to the motion planning problem for control affine systems by using trigonometric polynomials as control functions the class of systems under consideration satisfies the controllability rank condition with the lie brackets up to the second order the approach proposed here allows to reduce a point to point control problem to solving a system of algebraic equations the local solvability of that system is proved and formulas for the parameters of control functions are presented our local and global control design schemes are illustrated by several examples

topology optimization in wavelet space we investigate the use of wavelet methods for the design description in topology optimization this is a new setting for topology optimization that does not take the material densities in the elements of the finite element model as the design space this new approach has advantages and limitations which are discussed it is shown how the control of wavelet coefficients can be used to prevent the formation of checkerboard patterns and to obtain some geometry control problems related to overlapping basis functions are analysed and solution methods are proposed examples of optimized designs using the described methods are given copyright 2001 john wiley sons ltd

a new level set method for systematic design of hinge free compliant mechanisms abstract this paper presents a new level set based method to realize shape and topology optimization of hinge free compliant mechanisms a quadratic energy functional used in image processing applications is introduced in the level set method to control the geometric width of structural components in the created mechanism a semi implicit scheme with an additive operator splitting aos algorithm is employed to solve the hamilton jacobi partial differential equation pde in the level set method the design of compliant mechanisms is mathematically represented as a general non linear programming with a new objective function augmented by the high order energy term the structural optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints in doing so it is expected that numerical difficulties such as the courant friedrichs lewy cfl condition and periodically applied re initialization procedures in most conventional level set methods can be eliminated in addition new holes can be created inside the design domain the final mechanism configurations consist of strip like members suitable for generating distributed compliance and solving the de facto hinge problem in the design of compliant mechanisms two widely studied numerical examples are studied to demonstrate the effectiveness of the proposed method in the context of designing distributed compliant mechanisms

a new theoretical approach to absorbing layers we consider the construction of absorbing boundary layers using asymptotic expansions the small parameter being the width of the layer this allows us to define the order of the layer we compute layers of various orders and analyze their stability properties finally we perform some numerical tests to evaluate the practical utility of our layers

series expansions for the evolution of mechanical control systems this paper presents a series expansion that describes the evolution of a mechanical system starting at rest and subject to a time varying external force mechanical systems are presented as second order systems on a configuration manifold via the notion of affine connections the series expansion is derived by exploiting the homogeneity property of mechanical systems and the variations of constant formula a convergence analysis is obtained using some analytic functions and combinatorial analysis results this expansion provides a rigorous means of analyzing locomotion gaits in robotics and lays the foundation for the design of motion control algorithms for a large class of underactuated mechanical systems

local controllability in 3 manifolds small time local controllability of a two input ck affine control system on a 3 dimesional connected ck manifold m is studied showing that in general a necessary condition is also sufficient on an open dense subset of the set of points where it is verified an example shows a situation where the sufficient condition for small time local controllability of sussmann 8 cannot be applied but in which the method now presented distinguishes the possible cases

low order controllability and kinematic reductions for affine connection control systems controllability and kinematic modeling notions are investigated for a class of mechanical control systems first low order controllability results are given for the class of mechanical control systems second a precise connection is made between those mechanical systems which are dynamic i e have forces as inputs and those which are kinematic i e have velocities as inputs interestingly and surprisingly these two subjects are characterized and linked by a certain intrinsic vector valued quadratic form that can be associated to an affine connection control system

minimum time with bounded energy minimum energy with bounded time necessary and sufficient conditions for the regularity of the minimum time function and minimum energy function for a control system with controls in l p 0 infty bbb r m and p ge 1 are given in terms of topological properties of the reachable sets in particular standard local controllability assumptions are sufficient to yield the continuity of both value functions for linear systems and p ge1 and the holder continuity of the minimum time function for nonlinear systems and p 1

a polynomial approach to discrete time non linear system controllability this paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single input single output siso discrete time non linear systems the condition is presented in terms of common factors of a non commutative polynomial expression this extends the result on controllability of linear systems and the recent result on controllability of continuous time non linear systems to expose controllability of discrete time non linear systems in the input output framework the controllability condition yields a finite step computing procedure for examining controllability of discrete time input output non linear systems

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation

the complexity of deciding controllability abstract it is shown that the problem of deciding whether a control system is small time locally controllable or not is np hard this is an extension of a recent paper by sontag to single input systems and to bounded controls