In this paper we propose modeling and analysis techniques for genetic networks that provide biologists with insight into the dynamics of such systems. Central to our modeling approach is the framework of hybrid systems and our analysis tools are derived from formal analysis of such systems. Given a set of states characterizing a property of biological interestP , we present the Multi-Affine Rec...

Most robot control and planning algorithms are complex, involving a combination of reactive controllers, behavior-based controllers, and deliberative controllers. The switching between different behaviors or controllers makes such systems hybrid, i.e. combining discrete and continuous dynamics. While proofs of convergence, robustness and stability are often available for simple controllers unde...

This paper presents an algorithm which extends the rapidly-exploring random tree (RRT) framework to deal with change of the task environments. This algorithm called the Retrieval RRT Strategy (RRS) combines a support vector machine (SVM) and RRT and plans the robot motion in the presence of the change of the surrounding environment. This algorithm consists of two levels. At the first level, the...

For an environment to be well suited for wheelchair use not only should it be sufficiently clear of obstacles so that the wheelchair can navigate it, it should also be properly designed so that critical devices such as light switches can be reached by the hand of the wheelchair user. Given a goal location, explicitly calculating a path of the wheelchair and the person sitting in it so that they...

This paper proposes the use of a small differential robot with two DC motors, controlled by an ESP32 microcon-troller, that implements Rapidly Exploring Random Trees algorithm to navigate from origin point destination in unknown but observable environment. The motivation behind this research is explore low-cost, versatile and efficient robotic platform for autonomous navigation complex environm...

This paper presents several modifications to the basic rapidly-exploring random tree (RRT) search algorithm. The fundamental idea is to utilize a heuristic quality function to guide the search. Results from a relevant simulation experiment illustrate the benefit and drawbacks of the developed algorithms. The paper concludes with several promising directions for future research.

In many relevant path planning problems, loop closure constraints reduce the configuration space to a manifold embedded in the higher-dimensional joint ambient space. Whereas many progresses have been done to solve path planning problems in the presence of obstacles, only few work consider loop closure constraints. In this paper, we present the AtlasRRT algorithm, a planner specially tailored f...

In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.