simultaneous h control of a finite collection of linear plants with a single nonlinear digital controller abstract this paper considers the problem of simultaneous h control of a finite collection of linear time invariant systems via a nonlinear digital output feedback controller the main result is given in terms of the existence of suitable solutions to riccati algebraic equations and a dynamic programming equation our main result shows that if the simultaneous h control problem for k linear time invariant plants of orders n 1 n 2 n k can be solved then this problem can be solved via a nonlinear time invariant controller of order n n 1 n 2 n k

filtering closed curves a closed curve in the plane can be described in several ways we show that a simple representation in terms of radius of curvature versus normal direction has certain advantages in particular convolutional filtering of the extended circular image leads to a closed curve similar filtering operations applied to some other representations of the curve do not guarantee that the result corresponds to a closed curve in one case where a closed curve is produced it is smaller than the original a description of a curve can be based on a sequence of smoothed versions of the curve this is one reason why smoothing of closed curves is of interest

kinodynamic motion planning kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints in the general problem given a robot system we must find a minimal time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration we consider the simplified case of a point mass under newtonian mechanics together with velocity and acceleration bounds the point must be flown from a start to a goal amidst polyhedral obstacles in 2d or 3d although exact solutions to this problem are not known we provide the first provably good approximation algorithm and show that it runs in polynomial time

constructing roadmaps of semi algebraic sets i completeness abstract this paper describes preliminary work on an algorithm for planning collision free motions for a robot manipulator in the presence of obstacles the physical obstacles lead to forbidden regions in the robots configuration space and for collision free motion we need paths through configuration space which avoid these regions our method is to construct a certain one dimensional subset or roadmap of the space of allowable configurations if s denotes the set of allowable configurations the roadmap has the property that any connected component of s contains a single connected component of the roadmap it is also possible starting from an arbitrary point p s to rapidly construct a path from p to a point on the roadmap thus given any two points in s we can rapidly determine whether they lie in the same connected component of s and if they do we can return a candidate path between them we do not give a complete description of the algorithm here but we define the roadmap geometrically and verify that it has the necessary connectivity

using interval arithmetic to prove that a set is path connected in this paper we give a numerical algorithm able to prove whether a set s described by nonlinear inequalities is path connected or not to our knowledge no other algorithm numerical or symbolic is able to deal with this type of problem the proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as s examples illustrate the principle of the approach

robust finite horizon minimax filtering for discrete time stochastic uncertain systems we study a finite horizon robust minimax filtering problem for time varying discrete time stochastic uncertain systems the uncertainty in the system is characterized by a set of probability measures under which the stochastic noises driving the system are defined the optimal minimax filter has been found by applying techniques of risk sensitive lqg control the structure and properties of resulting filter are analyzed and compared to h and kalman filters

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

control parametrization a unified approach to optimal control problems with general constraints abstract in this paper we consider a class of optimal control problems with general constraints the aim is to provide a unified approach to the numerical solution of this general class of optimal control problems by using the control parametrization technique where different types of constraints are shown to be equivalent to essentially the same functional form as the cost functional some convergence properties of this proposed method are also investigated

the alpha method direct transcription in path constrained dynamic optimization numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions in many applications regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to useful control solutions for complex engineering problems with many constraints it is often difficult to find effective nondegenerate perturbations that produce useful solutions in some neighborhood of the correct solution in this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints for all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the original problem the regularization is quantifiable in terms of time step size in the mesh and the regularization parameter for fully regularized systems the scheme converges linearly in time step size the method is illustrated with examples

optimal control of underactuated nonholonomic mechanical systems in this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic underactuated mechanical systems in particular we aim to minimize the norm squared of the control input to move the system from an initial to a terminal state we consider systems evolving on general manifolds the class of nonholonomic systems we study in this paper includes in particular wheeled type vehicles which are important for many robotic locomotion systems the two special aspects of this optimal control problem are the nonholonomic constraints and underactuation nonholonomic constraints restrict the evolution of the system to a distribution on the manifold the nonholonomic connection is used to express the constrained equations of motion many robotic systems are underactuated since control inputs are usually applied through the robot s internal configuration space only while we do not consider symmetries with respect to group actions in this paper the fact that the system is underactuated is taken into account in our problem formulation this allows one to compute reaction forces due to any inputs applied in directions orthogonal to the constraint distribution we illustrate our ideas by considering a simple example on a three dimensional manifold including obstacle avoidance using the method of navigation functions

energy optimal trajectory planning for robot manipulators with holonomic constraints abstract in this paper we study two different trajectory planning problems for robot manipulators in the first case the end effector of the robot is constrained to move along a prescribed path in the workspace whereas in the second case the trajectory of the end effector has to be determined in the presence of obstacles constraints of this type are called holonomic constraints both problems have been solved as optimal control problems given the dynamic model of the robot manipulator the initial state of the system some specifications about the final state and a set of holonomic constraints one has to find the trajectory and the actuator torques that minimize the energy consumption during the motion the presence of holonomic constraints makes the optimal control problem particularly difficult to solve our method involves a numerical resolution of a reformulation of the constrained optimal control problem into an unconstrained calculus of variations problem in which the state space constraints and the dynamic equations also regarded as constraints are treated by means of special derivative multipliers we solve the resulting calculus of variations problem using a numerical approach based on the euler lagrange necessary condition in the integral form in which time is discretized and admissible variations for each variable are approximated using a linear combination of piecewise continuous basis functions of time the use of the euler lagrange necessary condition in integral form avoids the need for numerical corner conditions and the necessity of patching together solutions between corners in this way a general method for the solution of constrained optimal control problems is obtained in which holonomic constraints can be easily treated numerical results of the application of this method to trajectory planning of planar horizontal robot manipulators with two revolute joints are reported

nonlinear versus linear control in the robust stabilizability of linear uncertain systems via fixed order output feedback this paper considers the problem of robustly stabilizing an uncertain system via fixed order output feedback control this problem is considered by defining a notion of robust stabilizability with a quadratic storage function this notion is closely related to the notion of quadratic stabilizability the main result of the paper shows that if an uncertain system is robustly stabilizable with a quadratic storage function via a nonlinear time varying controller then it will also be robustly stabilizable with a quadratic storage function via a linear time invariant controller of the same order

on using lp to collision detection between a manipulator arm and surrounding obstacles abstract this paper is concerned with two linear programming lp models for the detection of a collision between a manipulator arm and its surrounding obstacles on the basis of a real case study in particular the first model finds the intersections between two convex polyhedra while the second one finds the intersections between suitable representations of the objects a comparison between the two approaches is presented on the basis of experimental data 9200 test cases have been analyzed

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

formulation and optimization of cubic polynomial joint trajectories for industrial robots because of physical constraints the optimum control of industrial robots is a difficult problem an alternative approach is to divide the problem into two parts optimum path planning for off line processing followed by on line path tracking the path tracking can be achieved by adopting the existing approach the path planning is done at the joint level cubic spline functions are used for constructing joint trajectories for industrial robots the motion of the robot is specified by a sequence of cartesian knots i e positions and orientations of the hand for an n joint robot these cartesian knots are transformed into n sets of joint displacements with one set for each joint piecewise cubic polynomials are used to fit the sequence of joint displacements for each of the n joints because of the use of the cubic spline function idea there are only n 2 equations to be solved for each joint where n is the number of selected knots the problem is proved to be uniquely solvable an algorithm is developed to schedule the time intervals between each pair of adjacent knots such that the total traveling time is minimized subject to the physical constraints on joint velocities accelerations and jerks fortran programs have been written to implement 1 the procedure for constructing the cubic polynomial joint trajectories and 2 the algorithm for minimizing the traveling time results are illustrated by means of a numerical example

constrained minimum time path planning for robot manipulators via virtual knots of the cubic b spline functions the b spline functions are used to generate the constrained minimum time path for a robot manipulator the interpolated path via b spline functions is determined via a unique set of virtual knots so that the robot path can pass every intermediate knot and satisfy the boundary conditions the local control property of the b spline functions can also be utilized to simplify the involved computational complexities the flexible polyhedron search algorithm is used to generate the near minimum time path with velocity acceleration and jerk constraints on every intermediate point this approach can simplify the formulation and procedures for generating the near minimum time cubic b spline path the use of this method to generate the constrained minimum time joint trajectories for a puma 560 robot is discussed as an example

structured dissipativity and absolute stability of nonlinear systems the paper considers a problem of absolute stability for a nonlinear uncertain system with structured uncertainty an s procedure for nonlinear systems is established and using this the paper shows that the absolute stability problem is equivalent to an absolute stability problem for a nonlinear uncertain system with unstructured uncertainty the paper also introduces a new notion of structured dissipativeness for nonlinear systems this notion extends the standard notion of dissipativeness in that it allows for multiple supply functions the paper shows that a nonlinear uncertain system containing structured uncertainties will be absolutely stable if and only if a corresponding structured dissipativeness condition is satisfied it is also shown that structured dissipativeness is equivalent to the standard notion of dissipativeness with a parameter dependent supply function

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

matching 3 d line segments with applications to multiple object motion estimation a two stage algorithm for matching line segments using three dimensional data is presented in the first stage a tree search based on the orientation of the line segments is applied to establish potential matches the sign ambiguity of line segments is fixed by a simple congruency constraint in the second stage a hough clustering technique based on the position of line segments is applied to verify potential matches any paired line segments of a match that cannot be brought to overlap by the translation determined by the clustering are removed from the match unlike previous methods this algorithm combats noise more effectively and ensures the global consistency of a match while the original motivation for the algorithm is multiple object motion estimation from stereo image sequences the algorithm can also be applied to other domains such as object recognition and object model construction from multiple views

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

a morphological approach to shortest path planning for rotating objects this paper presents a mathematical morphology based approach to find the shortest path of an arbitrarily shaped moving object with rotations amid obstacles of arbitrary shapes by utilizing the proposed rotational morphology along with the continuous turning angle constraint the representation framework of the motion planning problem becomes simple and practical two vehicle models with different driving and turning systems are used in solving the path planning problem and their strategies are presented simulation results show that our algorithm works successfully in various conditions

brief paper robust control with a terminal state constraint this paper introduces a problem of robust control with a terminal state constraint this problem involves finding an output feedback controller to steer the initial state of a given system into an ellipsoidal bounding set in a specified time the underlying system in this problem is a time varying uncertain linear system in which the uncertainty satisfies an integral quadratic constraint necessary and sufficient conditions are given for the solution to this problem in terms of a pair of parameter dependent riccati differential equations

multi grid methods for hamilton jacobi bellman equations in this paper we develop multi grid algorithms for the numerical solution of hamilton jacobi bellman equations the proposed schemes result from a combination of standard multi grid techniques and the iterative methods used by lions and mercier in 11 a convergence result is given and the efficiency of the algorithms is illustrated by some numerical examples

a new computational algorithm for functional inequality constrained optimization problems abstract in this note a computational algorithm is devised for solving a class of functional inequality constrained optimization problems based on a penalty function for illustration a numerical example is solved

h controller synthesis for pendulum like systems abstract this paper focus on a stabilization problem for a class of nonlinear systems with periodic nonlinearities called pendulum like systems a notion of lagrange stabilizability is introduced which extends the concept of lagrange stability to the case of controller synthesis based on this concept we address the problem of designing a linear dynamic output controller which stabilizes in the lagrange sense a pendulum like system within the framework of the h control theory lagrange stabilizability conditions for uncertainty free systems and systems with norm bounded uncertainty in the linear part are derived respectively when these conditions are satisfied the desired stabilization output feedback controller can be constructed via feasible solutions of a certain set of linear matrix inequalities lmis

convergence result for the constraint preserving mid point scheme for micromagnetism an important progress was recently done in numerical approximation of weak solutions to a micromagnetic model equation the problem with the nonconvex side constraint of preserving the length of the magnetization was tackled by using reduced integration several schemes were proposed and their convergence to weak solutions was proved all schemes were derived from the landau lifshitz gilbert form of the micromagnetic equation however when the precessional term in the original landau lifshitz ll form of the micromagnetic equation tends to zero the above schemes become unusable we propose a scheme derived from the mid point rule for the ll form of the micromagnetic equation combined with the reduced integration we show convergence to a weak solution of the ll equation and demonstrate the usefulness of the proposed scheme to study the limit process when the precessional parameter of the micromagnetic equation goes to zero

minimum time trajectory planning of mechanical manipulators under dynamic constraints the paper presents a global optimization approach to the trajectory planning problem of mechanical manipulators the purpose is to obtain a minimum time cubic spline trajectory subject to constraints given by limited joint torques and torque derivatives taking into account the non linear manipulator dynamics it is shown how without conservativeness a semi infinite optimization problem emerges conditions ensuring that the formalized problem admits a solution are given the estimated global solution can be actually obtained by means of an hybrid genetic interval algorithm that guarantees the feasibility of the found solution the methodology is illustrated with numerical details for a two link planar arm and a puma six link manipulator for the former comparisons with an alternative optimization solver are exposed

decentralized variable structure control for tracking in non linear systems the problem of tracking time varying trajectories in non linear systems is considered these trajectories could be generated on line by a reference model the problem is tackled by considering the overall system as a set of decentralized linear sub systems which can be modelled as a set of double integrators and treating the non linearities as uncertainties with known bounds on their magnitudes a variable structure controller is designed based on the theory of uncertain dynamical systems the system is shown to track a class of trajectories generated by the reference mode a set of double integrators to within a specified tolerance some analysis is presented to explain the dynamic behaviour of the closed loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty simulation results are presented to validate the conclusions

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part abstract systems with periodically nonstationary linear part are considered inputs and outputs of nonlinearities satisfy a certain integral quadratic constraint the conditions necessary and sufficient of dichotomy and absolute stability are obtained

robust output feedback constrained controllability of uncertain linear time varying systems abstract this paper introduces the concept of robust output feedback constrained controllability for a class of linear uncertain systems the uncertainty in the system is assumed to have a deterministic character and satisfy a certain integral quadratic constraint a necessary and sufficient condition for robust output feedback controllability is given in terms of the existence of suitable solutions to a riccati differential equation of the game type and a dynamic programming equation

a sensitivity approach to optimal spline robot trajectories abstract a robot trajectory planning problem is considered using smooth interpolating cubic splines as joint space trajectories the path is parameterized in terms of time intervals between knots a minimum time optimization problem is formulated under maximum torque and velocity constraints and is solved by means of a first order derivative type algorithm for semi infinite nonlinear programming feasible directions in the parameter space are generated using sensitivity coefficients of the active constraints numerical simulations are reported for a two link scara robot the proposed approach can be used for optimizing more general objective functions under different types of constraints

properties of min max controllers in uncertain dynamical systems we discuss properties of min max controllers previously obtained for uncertain dynamical systems in particular we present a new model for switching action and re examine asymptotic stability we demonstrate the attractiveness of switching surfaces and comment on the insensitivity of solutions in those surfaces to the uncertainty

darboux frames snakes and super quadrics geometry from the bottom up a representational and a computational model for deriving 3 d articulated volumetric descriptions of objects from laser rangefinder data is described this method is purely bottom up it relies on general assumptions cast in terms of differential geometry darboux frames snakes and superquadrics form the basis of this representation and curvature consistency provides the computational framework the organization is hierarchical darboux frames are used to describe the local surface whereas snakes are used to interpolate between features particularly those that serve to partition a surface into its constituent parts superquadrics are used to characterize the 3 d shape of each surface partition the result is a set of connected volumetric primitives that serve to describe the overall shape of an object examples that show how the approach performs on data acquired with a laser rangefinder are included

fuzzy distances for proximity characterization under uncertainty models of objects used in planning motions for robots are considered in this paper a fuzzy approach to handle imprecision in estimated object location is presented procedures for computing fuzzy distances between a pair of objects are developed the procedures are analyzed for their computational complexity the utility of the distance computations in reasoning about spatial relationships is illustrated

spatial planning a configuration space approach this paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects this problem arises in applications that require choosing how to arrange or how to move objects without collisions the approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space in which each coordinate represents a degree of freedom in the position or orientation of the object the configurations forbidden to this object due to the presence of other objects can then be characterized as regions in the configuration space called configuration space obstacles the paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra

a connection between h control and the absolute stabilizability of uncertain systems abstract this paper considers a stabilization problem for a class of uncertain systems in which the uncertainty satisfies a certain integral quadratic constraint such uncertain systems have been previously studied in the theory of absolute stability with most publications in this area being in the russian literature the paper introduces a notion of absolute stabilizability and shows that an uncertain system is absolutely stabilizable if and only if there exists a solution to a corresponding h control problem the paper also shows that if an uncertain system can be absolutely stabilized via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control

data smoothing and interpolation using eighth order algebraic splines a new type of algebraic spline is used to derive a filter for smoothing or interpolating discrete data points the spline is dependent on control parameters that specify the relative importance of data fitting and the derivatives of the spline a general spline of arbitrary order is first formulated using matrix equations we then focus on eighth order splines because of the continuity of their first three derivatives desirable for motor and robotics applications the spline s matrix equations are rewritten to give a recursive filter that can be implemented in real time for lengthy data sequences the filter is lowpass with a bandwidth that is dependent on the spline s control parameters numerical results including a simple image processing application show the tradeoffs that can be achieved using the algebraic splines

a dynamic programming approach to trajectory planning of robotic manipulators this paper presents a solution to the problem of minimizing the cost of moving a robotic manipulator along a specified geometric path subject to input torque force constraints taking the coupled nonlinear dynamics of the manipulator into account the proposed method uses dynamic programming dp to find the positions velocities accelerations and torques that minimize cost since the use of parametric functions reduces the dimension of the state space from 2n for an n jointed manipulator to two the dp method does not suffer from the curse of dimensionality while maintaining the elegance of our previous trajectory planning method we have developed the dp method for the general case where 1 the actuator torque limits are dependent on one another 2 the cost functions can have an arbitrary form and 3 there are constraints on the jerk or derivative of the acceleration also we have shown that the dp solution converges as the grid size decreases as numerical examples the trajectory planning method is simulated for the first three joints of the pacs arm which is a cylindrical arm manufactured by the bendix corporation

time optimal path tracking for robots a convex optimization approach this paper focuses on time optimal path tracking a subproblem in time optimal motion planning of robot systems through a nonlinear change of variables the time optimal path tracking problem is transformed here into a convex optimal control problem with a single state various convexity preserving extension are introduced resulting in a versatile approach for optimal path tracking a direct transcription method is presented that reduces finding the globally optimal trajectory to solving a second order cone program using robust numerical algorithms that are freely available validation against known examples and application to a more complex example illustrate the versatility and practicality of the new method

geometric optimization and the polynomial hierarchy we illustrate two different techniques of accurately classifying geometric optimization problems in the polynomial hierarchy we show that if np co np then there are interesting natural geometric optimization problems location allocation problems under minsum in 2 p that are in neither np nor co np hence all these problems are shown to belong properly to 2 p the second level of the polynomial hierarchy we also show that if np co np then there are again some interesting geometric optimization problems location allocation problems under minmax properly in 2 p and furthermore they are complete for a class dp which is contained in 2 p and contains np co np

robust control with rejection of harmonic disturbances this paper considers a finite time output feedback control problem for a class of uncertain systems subject to harmonic disturbances of known frequencies the controller is required to minimize a quadratic cost functional subject to the given uncertainties and harmonic disturbances the main result gives a necessary and sufficient condition for the existence of a suitable controller the condition is given terms of a pair of riccati differential equations which arise in a corresponding h sup spl infin control problem

three dimensional euclidean distance transformation and its application to shortest path planning in this paper we present a novel method to obtain the three dimensional euclidean distance transformation edt in two scans of the image the shortest path can be extracted based on the distance maps using the minimum value tracing the edt is obtained correctly and efficiently in a constant time for arbitrary types of images including the existence of obstacles by adopting the new dynamically rotational mathematical morphology we not only guarantee the collision free in the shortest path but also reduce the time complexity dramatically

an optimal one way multigrid algorithm for discrete time stochastic control the numerical solution of discrete time stationary infinite horizon discounted stochastic control problems is considered for the case where the state space is continuous and the problem is to be solved approximately within a desired accuracy after a discussion of problem discretization the authors introduce a multigrid version of the successive approximation algorithm that proceeds one way from coarse to fine grids and analyze its computational requirements as a function of the desired accuracy and of the discount factor they also study the effects of a certain mixing ergodicity condition on the algorithm s performance it is shown that the one way multigrid algorithm improves upon the complexity of its single grid variant and is in a certain sense optimal

a crank nicolson scheme for the landau lifshitz equation without damping an accurate and efficient numerical approach based on a finite difference method with crank nicolson time stepping is proposed for the landau lifshitz equation without damping the phenomenological landau lifshitz equation describes the dynamics of ferromagnetism the crank nicolson method is very popular in the numerical schemes for parabolic equations since it is second order accurate in time although widely used the method does not always produce accurate results when it is applied to the landau lifshitz equation the objective of this article is to enumerate the problems and then to propose an accurate and robust numerical solution algorithm a discrete scheme and a numerical solution algorithm for the landau lifshitz equation are described a nonlinear multigrid method is used for handling the nonlinearities of the resulting discrete system of equations at each time step we show numerically that the proposed scheme has a second order convergence in space and time

local optimization of dynamic programs with guaranteed satisfaction of path constraints an algorithm is proposed for locating a feasible point satisfying the kkt conditions to a specified tolerance of feasible inequality path constrained dynamic programs pcdp within a finite number of iterations the algorithm is based on iteratively approximating the pcdp by restricting the right hand side of the path constraints and enforcing the path constraints at finitely many time points the main contribution of this article is an adaptation of the semi infinite program sip algorithm proposed in mitsos 2011 to pcdp it is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first order kkt conditions of the pcdp to a specified tolerance the main assumptions are i availability of a nonlinear program nlp local solver that generates a kkt point of the constructed approximation to pcdp at each iteration if this problem is indeed feasible ii existence of a slater point of the pcdp that also satisfies the first order kkt conditions of the pcdp to a specified tolerance iii all kkt multipliers are nonnegative and uniformly bounded with respect to all iterations the performance of the algorithm is analyzed through two numerical case studies

brief paper optimal control problems with a continuous inequality constraint on the state and the control we consider an optimal control problem with a nonlinear continuous inequality constraint both the state and the control are allowed to appear explicitly in this constraint by discretizing the control space and applying a novel transformation a corresponding class of semi infinite programming problems is derived a solution of each problem in this class furnishes a suboptimal control for the original problem furthermore we show that such a solution can be computed efficiently using a penalty function method on the basis of these two ideas an algorithm that computes a sequence of suboptimal controls for the original problem is proposed our main result shows that the cost of these suboptimal controls converges to the minimum cost for illustration an example problem is solved

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on the problem of multiple mobile robots cluttering a workspace we consider the problem of multiple mobile robots navigating in a common workspace initially based on the premise that the costs of operation of the robots can be ignored results regarding the probability of collision of two point robots in the workspace are derived obviously these results depend on the geometry of the workspace and hence they are derived for workspaces with various geometries the results are then extended for two robots of finite dimensions the question are k 1 robots better than k is then considered based on two modes of operation namely the batch scheduled mode and the list scheduled mode various theoretical results are derived if the costs of operation of the robots can be ignored based on various computational results obtained we conjecture that the answer to the question is in the affirmative in both modes of operation finally by using the model of computation which includes the costs of operation of the robots the problem is revisited we have shown that for various geometries and revenue to cost ratios there are optimal finite values for the number of robots that can operate within the workspace expressions for these optimal values have been derived

a connection between h control and the absolute stabilizability of discrete time uncertain linear systems we consider the problem of stabilizing a class of uncertain discrete time systems in which the uncertainty satisfies a certain sum constraint we consider a notion of absolute stabilizability for discrete time systems and show that a necessary and sufficient condition for a discrete time uncertain system to be absolutely stabilizable is existence of a solution to a corresponding discrete time h control problem we also show that if it is possible to stabilize an uncertain system via nonlinear output feedback control then it is possible to absolutely stabilize it via linear output feedback control

a gauss seidel projection method for micromagnetics simulations abstract one of the main difficulties in micromagnetics simulation is the severe time step constraint introduced by the exchange field using standard explicit integrators leads to a physical time step of sub pico seconds which is often two orders of magnitude smaller than the fastest physical time scales direct implicit integrators require solving complicated coupled systems in this paper we introduce an implicit method whose complexity is comparable to solving the scalar heat equation implicitly this method is based on a combination of a gauss seidel implementation of a fractional step implicit solver for the gyromagnetic term and the projection method for the heat flow of harmonic maps this method allows us to carry out fully resolved calculations for the switching of the magnetization in micron sized elements

weak robust controllability and observability of uncertain linear systems this paper introduces notions of weak robust observability full information weak robust controllability and partial information weak robust controllability for a class of uncertain linear systems in which the uncertainty satisfies an integral quadratic constraint the paper gives characterizations of these properties in terms of the existence of suitable solutions to riccati differential equations of the type which occur in h sup spl infin control furthermore it is shown that the conditions of weak robust observability and full information weak robust controllability are necessary but not sufficient for partial information weak robust controllability

the adaptive convexification algorithm a feasible point method for semi infinite programming we present a new numerical solution method for semi infinite optimization problems its main idea is to adaptively construct convex relaxations of the lower level problem replace the relaxed lower level problems equivalently by their karush kuhn tucker conditions and solve the resulting mathematical programs with complementarity constraints this approximation produces feasible iterates for the original problem the convex relaxations are constructed with ideas from the alpha bb method of global optimization the necessary upper bounds for second derivatives of functions on box domains can be determined using the techniques of interval arithmetic where our algorithm already works if only one such bound is available for the problem we show convergence of stationary points of the approximating problems to a stationary point of the original semi infinite problem within arbitrarily given tolerances numerical examples from chebyshev approximation and design centering illustrate the performance of the method

an optimization algorithm for checking feasibility of robust h infinity control problem for linear time varying uncertain systems an algorithm for checking feasibility of the robust h control problem for systems with time varying norm bounded uncertainty is suggested this algorithm is an iterative procedure on each step of

guaranteed satisfaction of inequality state constraints in pde constrained optimization abstract optimal control problems with inequality path constraints ipcs are present in several engineering problems described by partial differential equations pde we propose an algorithm to solve pde constrained dynamic optimization problems with guaranteed satisfaction of ipcs the algorithm is based on a solution of a sequence of approximated dynamic optimization problems following the strategy of fu et al automatica 2015 for the approximation the path constraint is imposed only on a set of discrete points and is thus relaxed at the same time it is restricted by an adaptive back off and by the error bound of the pde solution the approximation is iteratively improved at iterations without violation the restriction is reduced at iterations with violation the point of maximal violation is added to the discrete set under mild assumptions we prove finite termination of the algorithm we test the algorithm on an optimal grade change of a tubular reactor

a hamiltonian approach to compute an energy efficient trajectory for a servomotor system this paper considers a nonlinear constrained optimal control problem ncocp originated from energy optimal trajectory planning of servomotor systems solving the exact optimal solution is challenging because of the nonlinear and switching cost function and various constraints this paper proposes a method to manage the switching cost function to establish a set of necessary conditions of an ncocp specifically a concept sub trajectory is introduced to match multiple hamiltonian due to switches in the cost function necessary conditions on the optimal trajectory are established as a union of conditions for all sub trajectories and weierstrass erdmann corner conditions between sub trajectories the set of feasible structures of optimal trajectories is further identified and represented by various state transition diagrams for the servomotor application a decomposition based shooting method is proposed to compute an optimal trajectory by solving multi point boundary value problems simulations and experiments validate the effectiveness of the methodology and the energy saving benefit

a new approach to robust control of hybrid systems over infinite time the paper presents a new approach to output feedback robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller an output feedback h sup spl infin control problem on an infinite time interval is considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h sup spl infin filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

receding horizon time optimal control for a class of differentially flat systems abstract a closed loop time optimal path following control scheme is proposed for a class of constrained differentially flat systems within a receding horizon framework a finite horizon optimisation problem is solved at each sample using available state feedback and feedforward path information irrespective of horizon length the proposed formulation guarantees exact path following moreover the requirements under which the proposed algorithm achieves minimum time path following are established simulations conducted with a rigid x y table model confirm the theoretical results

the adaptive convexification algorithm for semi infinite programming with arbitrary index sets a numerical solution method for semi infinite optimization problems with arbitrary not necessarily box shaped index sets is presented following the ideas of floudas and stein siam j optim 18 1187 1208 2007 convex relaxations of the lower level problem are adaptively constructed and then reformulated as mathematical programs with complementarity constraints and solved although the index set is arbitrary this approximation produces feasible iterates for the original problem the convex relaxations and needed parameters are constructed with ideas of the bb method of global optimization and interval methods it is shown that after finitely many steps an epsilon stationary point of the original semi infinite problem is reached a numerical example illustrates the performance of the proposed method

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

a trigonometric trajectory generator for robotic arms interpolation of a robot joint trajectory is realized using trigonometric splines this method is based on the assumption that joint space knots have been generated from cartesian knots by an inverse kinematics algorithm the use of trigonometric splines results in smooth joint trajectories and is amenable to real time obstacle avoidance some of the spline parameters can be chosen to minimize an objective function e g jerk or energy if the objective function is minimum jerk a closed form solution is obtained this paper introduces a trajectory interpolation algorithm discusses a method for trajectory optimization and includes simulation examples

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

adjoint sensitivity analysis for differential algebraic equations the adjoint dae system and its numerical solution an adjoint sensitivity method is presented for parameter dependent differential algebraic equation systems daes the adjoint system is derived along with conditions for its consistent initialization for daes of index up to two hessenberg for stable linear daes stability of the adjoint system for semi explicit daes or of an augmented adjoint system for fully implicit daes is shown in addition it is shown for these systems that numerical stability is maintained for the adjoint system or for the augmented adjoint system

global minimum time trajectory planning of mechanical manipulators using interval analysis the paper addresses the global minimum time trajectory planning of an m joint mechanical manipulator using a joint space scheme with given intermediate points to be interpolated by piecewise cubic polynomials a novel bisecting plane algorithm is proposed to schedule the times between adjacent knots under velocity acceleration and jerk constraints this algorithm which is proved to be globally convergent with certainty within an arbitrary precision uses an interval procedure a subroutine adopting tools and ideas of interval analysis in proving that a local minimum is actually a global one a worked example for the six joint case is exposed and computational results of a c implementation are included

variational analysis in semi infinite and infinite programming ii necessary optimality conditions this paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development canovas et al siam j optim 20 2009 pp 1504 1526 from the viewpoint of robust lipschitzian stability the main results establish necessary optimality conditions for broad classes of semi infinite and infinite programs where objectives are generally described by nonsmooth and nonconvex functions on banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets the results obtained are new in both smooth and nonsmooth settings of semi infinite and infinite programming we illustrate our model and results by considering a practically meaningful model of water resource optimization via systems of reservoirs

collision detection for moving polyhedra we consider the collision detection problem for a three dimensional solid object moving among polyhedral obstacles the configuration space for this problem is six dimensional and the traditional representation of the space uses three translational parameters and three angles typically euler angles the constraints between the object and obstacles then involve trigonometric functions we show that a quaternion representation of rotation yields constraints which are purely algebraic in a seven dimensional space by simple manipulation the constraints may be projected down into a six dimensional space with no increase in complexity the algebraic form of the constraints greatly simplifies computation of collision points and allows us to derive an efficient exact intersection test for an object which is translating and rotating among obstacles

on information invariants in robotics we consider the problem of determining the information requirements to perform robot tasks using the concept ofinformation invariants this paper represents our attempt to characterize a family of complicated and subtle issues concerned with measuring robot task complexity we also provide a first approximation to a purely operational theory that addresses a narrow but interesting special case we discuss several measures for the information complexity of a task a how much internal state should the robot retain b how many cooperating agents are required and how much communication between them is necessary c how can the robot change side effect the environment in order to record state or sensory information to perform a task d how much information is provided by sensors and e how much computation is required by the robot we consider how one might develop a kind of calculus on a e in order to compare the power of sensor systems analytically to this end we attempt to develop a notion of information invariants we develop a theory whereby one sensor can be reduced to another much in the spirit of computation theoretic reductions by adding deleting and reallocating a e among collaborating autonomous agents

geometric reasoning about mechanical assembly abstract in which order can a product be assembled or disassembled how many hands are required how many degrees of freedom what parts should be withdrawn to allow the removal of a specified subassembly to answer such questions automatically important theoretical issues in geometric reasoning must be addressed this paper investigates the planning of assembly algorithms specifying dis assembly operations on the components of a product and the ordering of these operations it also presents measures to evaluate the complexity of these algorithms and techniques to estimate the inherent complexity of a product the central concept underlying these planning and complexity evaluation techniques is that of a non directional blocking graph a qualitative representation of the internal structure of an assembly product this representation describes the combinatorial set of parts interactions in polynomial space it is obtained by identifying physical criticalities where geometric interferences among parts change it is generated from an input geometric description of the product the main application considered in the paper is the creation of smart environments to help designers create products that are easier to manufacture and service other possible applications include planning for rapid prototyping and autonomous robots

on the piano movers problem i the case of a two dimensional rigid polygonal body moving amidst polygonal barriers we present an algorithm that solves a two dimensional case of the following problem which arises in robotics given a body b and a region bounded by a collection of walls either find a continuous motion connecting two given positions and orientations of b during which b avoids collision with the walls or else establish that no such motion exists the algorithm is polynomial in the number of walls o n5 if n is the number of walls but for typical wall configurations can run more efficiently it is somewhat related to a technique outlined by reif

robust state estimation for a class of uncertain time delay systems this paper considers a robust state estimation problem for a class of uncertain time delay systems in this problem the noise and uncertainty are modelled deterministically via an integral quadratic constraint the robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint this set is found to be an ellipsoid which is constructed via a linear state estimator

on determining optimal strategies in pursuit games in the plane pursuit games have application to robotics the pursuer models a moving obstacle and the evader models a robot that tries to reach a goal region without colliding with the moving obstacle at each moment the robot does not know the future trajectory of the obstacle the motion of the pursuer and the evader is controlled by their sets of permissible velocities called indicatrices we allow indicatrices that are more general than the simple motion i e velocities are bounded by an l2 norm circle we provide sufficient condition for a pursuit game to have value in this case we give optimal strategies for the pursuer and the evader we prove that the pursuit game in which the pursuer and the evader are convex objects moving with simple motion has value

qualitative rigid body mechanics abstract we present a theory of qualitative rigid body mechanics and describe a program that uses this theory to compute qualitative rigid body dynamic simulations the program works directly from a qualitative representation of geometry qualitative configuration space without need of any metric information the program can handle devices that are composed of an arbitrary number of fixed axis components and springs with driving inputs coming from both applied motions and forces the program employs quasi static assumptions i e inertia free motion inelastic collisions and frictionless contacts it employs a new qualitative representation for forces that reduces ambiguity in force sums and hence reduces unnecessary branching

a search algorithm for motion planning with six degrees of freedom abstract the motion planning problem is of central importance to the fields of robotics spatial planning and automated design in robotics we are interested in the automatic synthesis of robot motions given high level specifications of tasks and geometric models of the robot and obstacles the movers problem is to find a continuous collision free path for a moving object through an environment containing obstacles we present an implemented algorithm for the classical formulation of the three dimensional movers problem given an arbitrary rigid polyhedral moving object p with three translational and three rotational degrees of freedom find a continuous collision free path taking p from some initial configuration to a desired goal configuration this paper describes an implementation of a complete algorithm at a given resolution for the full six degree of freedom movers problem the algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six dimensional configuration space called c space the c space obstacles which characterize the physically unachievable configurations are directly represented by six dimensional manifolds whose boundaries are five dimensional c surfaces by characterizing these surfaces and their intersections collision free paths may be found by the closure of three operators which i slide along five dimensional level c surfaces parallel to c space obstacles ii slide along one to four dimensional intersections of level c surfaces and iii jump between six dimensional obstacles these operators are employed by a best first search algorithm in c space we will discuss theoretical properties of the algorithm including completeness at a resolution this paper describes the heuristic search with particular emphasis on the heuristic strategies that evaluate local geometric information at the heart of this paper lie the design and implementation of these strategies for planning paths along level c surfaces and their intersection manifolds and for reasoning about motions with three degrees of rotational freedom the problems of controlling the interaction of these strategies and of integrating diverse local experts for geometric reasoning provide an interesting application of search to a difficult domain with significant practical implications the representations and algorithms we develop impact many geometric planning problems and extend to cartesian manipulators with six degrees of freedom

brief paper simplified time optimal path planning of x y gantry systems along circular paths in this paper we consider time optimal path planning for x y gantry systems along circular paths in which acceleration and jerk limitations of each actuator are taken into full account the physical limitations are expressed as highly nonlinear state input constraints and are mathematically very difficult to handle effectively in this context we formulate the time optimal problem under reasonably simplified constraints and derive its solution in feedback form numerical examples demonstrate that the proposed time optimal circular path planning method decreases the traverse time significantly compared to the well known s curve method

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

relaxation based bounds for semi infinite programs finite formulations are presented for the calculation of lower and upper bounds on the optimal solution value of semi infinite programs sips involving smooth potentially nonconvex objective function and constraints the lower bounding problem is obtained by a formulation that combines the first and second order kkt necessary conditions of the lower level problem with a discretization of the parameter set the resulting mathematical program with equilibrium constraints mpec is a relaxation of the original sip and furnishes valid lower bounds if the parameter set is subdivided the optimal solution value of the lower bounding problem converges to the optimal solution value of the sip the upper bounding problem is based on convex and linear relaxations of the lower level problem resulting in a restriction of the sip if the parameter set is subdivided the constructed relaxations converge to the original lower level program the existence of sip slater points ensures convergence of the upper bounding problems to the optimal solution value of the sip several alternatives for the upper bounding problem are presented and discussed numerical results are presented for a number of test problems from the literature