Reachability Constraints Research Articles

Transient inter-production scheduling based on Petri nets and constraint programming

In this article, we focus on the transient inter-production scheduling problem between two cyclic productions in the framework of flexible manufacturing systems. This problem is first formulated as a reachability problem in timed Petri nets (TPN), then solved using a methodology based on constraint programming. Our work is based on the controlled executions proposed by Chretienne to model the sequence of transition firing dates. Our methodology is based on a preliminary resolution of the state equation between initial and final states in the underlying non-TPN. Then, we choose a duration T max corresponding to the maximal duration time of the scheduling. For each solution S of the state equation, we build a controlled execution from the sequence of firings in S. After the propagation of firing date constraints and reachability constraints in the TPN, we use constraint programming to enumerate the set of feasible controlled executions.

Unbounded Protocol Compliance Verification Using Interval Property Checking With Invariants

We propose a methodology to formally prove protocol compliance for communication blocks in System-on-Chip (SoC) designs. In this methodology, a set of operational properties is specified with respect to the states of a central finite state machine (FSM). This central FSM is called main FSM and controls the overall behavior of the design. In order to prove a set of compliance properties, we developed an approach that combines property checking on a bounded circuit model with an approximate reachability analysis. The property checker determines whether a property is valid for an arbitrary state of the design regardless of its reachability. In order to avoid false negatives, reachability constraints are added to the property, which are generated by an approximate FSM traversal algorithm. We show how the existence of a main FSM can be exploited systematically in the reachability analysis and how to partition both the transition relation and the state space such that the computational complexity is reduced drastically. This makes formal verification of protocol compliance tractable even for large designs with several thousand state variables. Our approach has been applied successfully to verify several industrial designs.

Tightened reachability constraints for the verification of linear hybrid systems

In this paper, we first generalize reachability constraints for linear differential equations, then tighten them by using the information of multiplicity of the eigenvalues and eigenvectors of such equations and put them into our constraint based approach for safety verification of hybrid systems that employs recursive reasoning to improve the method of constraint propagation based abstraction refinement.

Constrained Optimization of Multi-Degree-of-Freedom Mechanisms for Near-Time-Optimal Motions

This paper presents a method to design multi-degree-of-freedom mechanisms for near-time optimal motions. The design objective is to select system parameters, such as link lengths and actuator sizes, that will minimize the optimal motion time of the mechanism along a given path. The exact time-optimization problem is approximated by a simpler procedure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, and the reachability constraints as explicit functions of the design parameters, we transform the constrained optimization to a simpler curve-fitting procedure. This problem is formulated analytically, permitting the use of efficient gradient-based optimizations instead of the zero order optimization that is otherwise required. It is shown that with the appropriate choice of variables, the reachability constraints for planar mechanisms are linear in the design parameters. Consequently, the reachability of the entire path can be guaranteed by satisfying the reachability of only two extreme points along the path. This greatly simplifies the optimization problem since it reduces the dimensionality of the constraints and it permits the use of efficient projection methods. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency of the constrained optimization over previous penalty-based methods.