Time-optimal control for discrete-time hybrid automata

In this paper, the problem of time-optimal control for hybrid systems with discrete-time dynamics is considered. The hybrid controller steers all trajectories starting from a maximal set to a given target set in minimum time. We derive an algorithm that computes this maximal winning set. Also, algorithms for the computation of level sets associated with the value function rather than the value function itself are presented. We show that by solving the reachability problem for the discrete time hybrid automata we obtain the time optimal solution as well. The control synthesis is subject to hard constraints on both control inputs and states. For linear discrete-time dynamics, linear programming and quantifier elimination techniques are employed for the backward reachability analysis. Emphasis is given on the computation of operators for non-convex sets using an extended convex hull approach. A two-tank example is considered in order to demonstrate the techniques of the paper.     

Geometrically exact physics-based modeling and computer animation of highly flexible 1D mechanical systems

This paper presents a geometrically exact beam theory and a corresponding displacement-based finite-element model for modeling, analysis and natural-looking animation of highly flexible beam components of multibody systems undergoing huge static/dynamic rigid-elastic deformations. The beam theory fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, concepts of local displacements and orthogonal virtual rotations, and three Euler angles to exactly describe the coordinate transformation between the undeformed and deformed configurations. To demonstrate the accuracy and capability of this nonlinear beam element, nonlinear static and dynamic analysis of two highly flexible beams are performed, including the twisting a circular ring into three small rings and the spinup of a flexible helicopter rotor blade (Graphical abstract). These numerical results reveal that the proposed nonlinear beam element is accurate and versatile for modeling, analysis and 3D rendering and animation of multibody systems with highly flexible beam components.     

Example-driven animation synthesis

We introduce an easy and intuitive approach to create animations by assembling existing animations. Using our system, the user needs only to simply scribble regions of interest and select the example animations that he/she wants to apply. Our system will then synthesize a transformation for each triangle and solve an optimization problem to compute the new animation for this target mesh. Like playing a jigsaw puzzle game, even a novice can explore his/her creativity by using our system without learning complicated routines, but just using a few simple operations to achieve the goal.     

Continuity controlled hybrid automata

We investigate the connections between the process algebra for hybrid systems of Bergstra and Middelburg and the formalism of hybrid automata of Henzinger et al. We give interpretations of hybrid automata in the process algebra for hybrid systems and compare them with the standard interpretation of hybrid automata as timed transition systems. We also relate the synchronized product operator on hybrid automata to the parallel composition operator of the process algebra. It turns out that the formalism of hybrid automata matches a fragment of the process algebra for hybrid systems closely. We present an adaptation of the formalism of hybrid automata that yields an exact match.     

Inclusion dynamics hybrid automata

Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete state-transition systems such as finite state automata. A convenient and popular model, called hybrid automata, was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting. Intuitively, a hybrid automaton is simply a “finite-state” automaton with each state augmented by continuous variables, which evolve according to a set of well-defined continuous laws, each specified separately for each state. This article investigates both the notion of hybrid automaton and the model checking problem over such a structure. In particular, it relates first-order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions (x′f(x,t)) to a decidability problem for first-order formulæ over the reals. Furthermore, the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first-order formulæ over the reals. Despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite, we show that our techniques permit effective model checking for a nontrivial fragment of CTL.     

Dynamic free-form deformations for animation synthesis

Free form deformations (FFDs) are a popular tool for modeling and keyframe animation. The paper extends the use of FFDs to a dynamic setting. Our goal is to enable normally inanimate graphics objects, such as teapots and tables, to become animated, and learn to move about in a charming, cartoon like manner. To achieve this goal, we implement a system that can transform a wide class of objects into dynamic characters. Our formulation is based on parameterized hierarchical FFDs augmented with Lagrangian dynamics, and provides an efficient way to animate and control the simulated characters. Objects are assigned mass distributions and elastic deformation properties, which allow them to translate, rotate, and deform according to internal and external forces. In addition, we implement an automated optimization process that searches for suitable control strategies. The primary contributions of the work are threefold. First, we formulate a dynamic generalization of conventional, geometric FFDs. The formulation employs deformation modes which are tailored by the user and are expressed in terms of FFDs. Second, the formulation accommodates a hierarchy of dynamic FFDs that can be used to model local as well as global deformations. Third, the deformation modes can be active, thereby producing locomotion     

Learnt inverse kinematics for animation synthesis

Existing work on animation synthesis can be roughly split into two approaches, those that combine segments of motion-capture data, and those that perform inverse kinematics. In this paper, we present a method for performing animation synthesis of an articulated object (e.g. human body and a dog) from a minimal set of body joint positions, following the approach of inverse kinematics. We tackle this problem from a learning perspective. Firstly, we address the need for knowledge on the physical constraints of the articulated body, so as to avoid the generation of a physically impossible poses. A common solution is to heuristically specify the kinematic constraints for the skeleton model. In this paper however, the physical constraints of the articulated body are represented using a hierarchical cluster model learnt from a motion capture database. Additionally, we shall show that the learnt model automatically captures the correlation between different joints through simultaneous modelling of their angles. We then show how this model can be utilised to perform inverse kinematics in a simple and efficient manner. Crucially, we describe how IK is carried out from a minimal set of end-effector positions. Following this, we show how this “learnt inverse kinematics” framework can be used to perform animation syntheses on different types of articulated structures. To this end, the results presented include the retargeting of a flat surface walking animation to various uneven terrains to demonstrate the synthesis of a full human body motion from the positions of only the hands, feet and torso. Additionally, we show how the same method can be applied to the animation synthesis of a dog using only its feet and torso positions.     

Dynamical properties of hybrid automata

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results on existence, uniqueness, and continuity serve as a starting point for stability analysis. Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata.     

Efficient parallel automata construction for hybrid resource-impelled data-matching

We are presenting an innovative, massively-parallel heterogeneous architecture for the very fast construction and implementation of very large Aho–Corasick and Commentz-Walter pattern-matching automata, commonly used in data-matching applications, and validate its use with large sets of data actively used in intrusion detection systems. Our approach represents the first known hybrid-parallel model for the construction of such automata and the first to allow self-adjusting pattern-matching automata in real-time by allowing full-duplex transfers at maximum throughput between the host (CPU) and the device (GPU). The architecture we propose is easily scalable to multi-GPU and multi-CPU systems and benefits greatly from GPU acceleration, also relying on a highly-efficient storage model for the automata and includes on-demand support for regular-expression matching, as well as support for custom heuristics to be built on top of the architecture, at different processing stages.     

Convergence analysis of hybrid cellular automata for topology optimization

The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence.     

Compositional synthesis of asynchronous automata

Asynchronous automata are a model of communication processes with a control structure distributed on a set P of processes, global initializations and global accepting conditions. The well-known theorem of Zielonka states that they recognize exactly the class of regular Mazurkiewicz trace languages. The corresponding synthesis problem is, given a global specification A of any regular trace language L, to build an asynchronous automaton that recognizes L, automatically. Yet, all such existing constructions are quite involved and yield an explosion of the number of states in each process, which is exponential in both the sizes of A and P. In this paper, we introduce the particular case of distributed asynchronous automata, which require that the initializations and the accepting conditions are distributed as well. We present an original technique based on simple compositions/decompositions of these distributed asynchronous automata that results in the construction of smaller non-deterministic asynchronous automata: now, the number of states in each process is only polynomial in the size of A, but is still exponential in the size of P.     

Engineering constraint solvers for automatic analysis of probabilistic hybrid automata

In this article, we recall different approaches to the constraint-based, symbolic analysis of hybrid discrete-continuous systems and combine them to a technology able to address hybrid systems exhibiting both non-deterministic and probabilistic behavior akin to infinite-state Markov decision processes. To enable mechanized analysis of such systems, we extend the reasoning power of arithmetic satisfiability-modulo-theories (SMT) solving by, first, reasoning over ordinary differential equations (ODEs) and, second, a comprehensive treatment of randomized (also known as stochastic) quantification over discrete variables as well as existential quantification over both discrete and continuous variables within the mixed Boolean-arithmetic constraint system. This provides the technological basis for a constraint-based analysis of dense-time probabilistic hybrid automata, extending previous results addressing discrete-time automata [33]. Generalizing SMT-based bounded model-checking of hybrid automata [5], [31], stochastic SMT including ODEs permits the direct analysis of probabilistic bounded reachability problems of dense-time probabilistic hybrid automata without resorting to approximation by intermediate finite-state abstractions.     

Synthesis of supervisory controllers for hybrid systems based onapproximating automata

The paper concerns the synthesis of supervisory controllers for a class of continuous-time hybrid systems with discrete-valued input signals that select differential inclusions for continuous-valued state trajectories and event-valued output signals generated by threshold crossings in the continuous state space, the supervisor is allowed to switch the input signal value when threshold events are observed. The objective is to synthesize a nonblocking supervisor such that the set of possible sequences of control and threshold event pairs for the closed-loop system lies between given upper and lower bounds in the sense of set containment. We show how this problem can be converted into a supervisor synthesis problem for a standard controlled discrete-event system (DES). A finite representation may not exist for the exact DES model of the hybrid system, however. To circumvent this difficulty, we present an algorithm for constructing finite-state Muller automata that accept outer approximations to the exact controlled threshold-event language, and we demonstrate that supervisors that solve the synthesis problem for the approximating automata achieve the control specifications when applied to the original hybrid system     

Loop reduction techniques for reachability analysis of linear hybrid automata

The problem of reachability analysis of linear hybrid automata(LHA) is very difficult.This paper considers to improve the efficiency of the reachability analysis by optimizing the structures of LHA.We identify two types of loops called the flexible loops and the zero loops,and present the techniques to replace the repetitions of those loops in the behavior of LHA with finite sequences of locations and in the meantime simplify the associated constraints.The techniques work not only for the polyhedral computing based algorithms but also for the bounded model checkers.     

Improved hybrid cellular automata for crashworthiness optimization of thin-walled structures

Thin-walled structures are of great importance in automotive crashworthiness design, because of their high crash energy absorption capability and their high potential for light weighting. To identify the best compromise between these two requirements, numerical optimization is needed. Size and shape optimization is relatively well explored while topology optimization for crash is still an open issue. Hence, this paper proposes an approach based on hybrid cellular automata (HCA) for crashworthiness topology optimization with a special focus on thin-walled structures. First approaches have been published, e.g. Duddeck et al. (Struct Multidiscip Optim 54(3):415–428, 2016), using a simple rule to define the target mass for the inner loop of the HCA. To improve the performance, a modified scheme is proposed here for the outer optimization loop, which is based on a bi-section search with limited length. In the inner loop, hybrid updating rules are used to redistribute the mass and a mass correction technique is proposed to make the real mass converge to the target mass strictly. The efficiency and correctness of the proposed method is compared with LS-OPT for axial crash case. Two different methods of defining the target mass in the outer loop are studied, the proposed bi-section search with limited length shows its advantage in two types of three-point bending crash optimization cases. Another advantage of this method is that it requires no significantly increasing number of evaluations when the number of design variables increases. This is demonstrated by applying this method to a crashworthiness optimization problem with 380 design variables.     

Lightweight wrinkle synthesis for 3D facial modeling and animation

We present a lightweight non-parametric method to generate wrinkles for 3D facial modeling and animation. The key lightweight feature of the method is that it can generate plausible wrinkles using a single low-cost Kinect camera and one high quality 3D face model with details as the example. Our method works in two stages: (1) offline personalized wrinkled blendshape construction. User-specific expressions are recorded using the RGB-Depth camera, and the wrinkles are generated through example-based synthesis of geometric details. (2) Online 3D facial performance capturing. These reconstructed expressions are used as blendshapes to capture facial animations in real-time. Experiments on a variety of facial performance videos show that our method can produce plausible results, approximating the wrinkles in an accurate way. Furthermore, our technique is low-cost and convenient for common users.