Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete
نویسندگان
چکیده
RRTs are a popular method for kinodynamic planning that many consider to be probabilistically complete. However, different variations of the RRT algorithm exist and not all of them are probabilistically complete. The tree can be extended using a fixed or variable time step. The input can be chosen randomly or the best input can be chosen such that the new child node is as close as possible to the sampled state according to the used distance metric. It has been shown that for finite input sets an RRT using a fixed step size with a randomly selected input is probabilistically complete. However, this variant is uncommon since it is less efficient. We prove that the more common variant of choosing the best input in combination with a fixed time step is not probabilistically complete.
منابع مشابه
A Quadratic Regulator - Based Heuristic for Rapidly Exploring State Space by Elena
Kinodynamic planning algorithms like Rapidly-Exploring Randomized Trees (RRTs) hold the promise of finding feasible trajectories for rich dynamical systems with complex, non-convex constraints. In practice, these algorithms perform very well on configuration space planning, but struggle to grow efficiently in systems with dynamics or differential constraints. This is due in part to the fact tha...
متن کاملDesign and Analysis of Step Stress Accelerated Life Tests for Censored Data}
Life testing often is consuming a very long time for testing. Therefore, the engineers and statisticians are looking for some approaches to reduce the running time. There is a recommended method for reducing the time of failure, such that the stress level of the test units will increase, and then they will fail earlier than normal operating conditions. These approaches are called accelerated li...
متن کاملRandomized Kinodynamic Planning
LaValle & Kuffner [] present an application of a randomized technique to the problem of kinodynamic planning. Their algorithm constructs Rapidly-exploring Random Trees (RRTs) in a high dimensional state space that encompasses both first order constraints resulting from the physically-based system dynamics as well as global kinematic constraints due to obstacles in the environment. By coupling...
متن کاملتوسعه یک روش عددی حجم محدود برای ارزیابی عملکرد هیدرودینامیکی سازه های دریایی
Development of a compatible computational fluid dynamics procedure to investigate rigid and fixed/free coastal and offshore structures hydrodynamics in a time-dependent one/two phase flow of viscous incompressible fluids is presented. Differential governing equations are discretised using finite volume approach based on a colocated arrangement. The conservation equations for mass and momentum a...
متن کاملTesting of Symbolic-Probabilistic Systems
We consider the testing of systems where probabilistic information is not given by means of fixed values but as sets of probabilities. We will use an extension of finite state machine where choices among transitions having the same input actions are probabilistically resolved. We will introduce our notion of test and we will define how tests are applied to the implementation under test (IUT). W...
متن کامل