Risk Analysis of Stochastic PERT Graph

Purpose of the article: The paper deals with a time and probability analysis of stochastic graph PERT. The paper focuses on the comparison of two different approaches calculation of probability analysis. Concretely the planning time of the project was calculated. A sample PERT network graph was examined, which comprised 18 nodes and 18 real activities and 6 fictions activities. For the purpose of the analysis, the basic characteristic times were calculated in accordance with traditional approaches related to the PERT method. Methodology/methods: The implementation of the PERT algorithm is based on the critical path method (CPM). It was calculated the basic time charactetistics of the project and identificed the critical path. For probability analysis was also calculated expected value, variance and standard deviance of the activities. For calculation of the planning time was used distribution function of standardized normal distribution. The PERT algorithm is realized by using spreadsheet in the MS Excel. Scientific aim: of the paper is comparison of two different approaches calculation of the probability analysis and their influence on the calculation of the planning time of the project. Findings: Two different approaches calculation of the probability analysis shows on different result of values of project planning time. Approach II better reflects the difference between the values of variances of project activities. The value of variance depends on the input values of three time durations s activity estimates (pessimistic, most likely, optimistic). For higher values of probability there is a bigger difference between the values of planned times that are calculated by two described approaches. Conclusions: The problem was solved using the example project whose model (network graph) contained 18 nodes and 24 activities. For each activity have been known three time estimates (pesimitic, most likely, optimistic). Based on these estimates were calculated expected values of the duration activities and their variances. Expected values of the duration activities were used as input values to calculate the time characteristics. Variances of the activities were used as input values to calculate the variance at the nodes. For these calculations two approaches was used. The expected value of project duration (value of earliest time in last node) was the same for both approaches. For the approach I is a value of the variance in the last node less than for the approach II. These values were used as input data for calculation of planning time of the project at various levels of probability according to the standardized normal distribution. From obtained results dependence between the probability and size of the differences in planned times were observed. This difference increases with a probability going to one. Based on the analysis a recommendation shows to use the approach II under conditions when there are large variations between optimistic (pessimistic) estimates of activity durations and the most likely estimate of activity duration. It causes great differences in values of the variances of the activities. The approach II better reflects this dissimilarity in the variances of the activities. This approach provides longer planning times of the project opposite the approach I

Optimal Relative Path Planning for Constrained Stochastic Space Systems

Rendezvous and proximity operations for automated spacecraft systems requires advanced path planning techniques that are capable of generating optimal paths. Real-world constraints, such as sensor noise and actuator errors, complicate the planning process. Operations also require flight safety considerations in order to prevent the spacecraft from potentially colliding with the associated companion spacecraft. This work proposes a new, ground-based trajectory planning approach that seeks an optimal trajectory while meeting all mission constraints and accounting for vehicle performance and safety requirements. This approach uses a closed-loop linear covariance simulation of the relative trajectory coupled with a genetic algorithm to determine fuel optimal trajectories. Spacecraft safety is addressed using statistical data from the linear covariance model to bound the probability of collision

A New Real-Time Path Planning Method Based on the Belief Space

A new approach of real-time path planning based on belief space is proposed, which solves the problems of modeling the real-time detecting environment and optimizing in local path planning with the fusing factors. Initially, a double-safe-edges free space is defined for describing the sensor detecting characters, so as to transform the complex environment into some free areas, which can help the robots to reach any positions effectively and safely. Then, based on the uncertainty functions and the transferable belief model (TBM), the basic belief assignment (BBA) spaces of each factor are presented and fused in the path optimizing process. So an innovative approach for getting the optimized path has been realized with the fusing the BBA and the decision making by the probability distributing. Simulation results indicate that the new method is beneficial in terms of real-time local path planning

Position-based Dynamics Simulator of Brain Deformations for Path Planning and Intra-Operative Control in Keyhole Neurosurgery

Many tasks in robot-assisted surgery require planning and controlling manipulators' motions that interact with highly deformable objects. This study proposes a realistic, time-bounded simulator based on Position-based Dynamics (PBD) simulation that mocks brain deformations due to catheter insertion for pre-operative path planning and intra-operative guidance in keyhole surgical procedures. It maximizes the probability of success by accounting for uncertainty in deformation models, noisy sensing, and unpredictable actuation. The PBD deformation parameters were initialized on a parallelepiped-shaped simulated phantom to obtain a reasonable starting guess for the brain white matter. They were calibrated by comparing the obtained displacements with deformation data for catheter insertion in a composite hydrogel phantom. Knowing the gray matter brain structures' different behaviors, the parameters were fine-tuned to obtain a generalized human brain model. The brain structures' average displacement was compared with values in the literature. The simulator's numerical model uses a novel approach with respect to the literature, and it has proved to be a close match with real brain deformations through validation using recorded deformation data of in-vivo animal trials with a mean mismatch of 4.73$\pm$2.15%. The stability, accuracy, and real-time performance make this model suitable for creating a dynamic environment for KN path planning, pre-operative path planning, and intra-operative guidance.Comment: 8 pages, 8 figures. This article has been accepted for publication in a future issue of IEEE Robotics and Automation Letters, but has not been fully edited. Content may change prior to final publication. 2377-3766 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. A. Segato and C. Di Vece equally contribute

Mobile agent path planning under uncertain environment using reinforcement learning and probabilistic model checking

The major challenge in mobile agent path planning, within an uncertain environment, is effectively determining an optimal control model to discover the target location as quickly as possible and evaluating the control system's reliability. To address this challenge, we introduce a learning-verification integrated mobile agent path planning method to achieve both the effectiveness and the reliability. More specifically, we first propose a modified Q-learning algorithm (a popular reinforcement learning algorithm), called Q EA−learning algorithm, to find the best Q-table in the environment. We then determine the location transition probability matrix, and establish a probability model using the assumption that the agent selects a location with a higher Q-value. Secondly, the learnt behaviour of the mobile agent based on Q EA−learning algorithm, is formalized as a Discrete-time Markov Chain (DTMC) model. Thirdly, the required reliability requirements of the mobile agent control system are specified using Probabilistic Computation Tree Logic (PCTL). In addition, the DTMC model and the specified properties are taken as the input of the Probabilistic Model Checker PRISM for automatic verification. This is preformed to evaluate and verify the control system's reliability. Finally, a case study of a mobile agent walking in a grids map is used to illustrate the proposed learning algorithm. Here we have a special focus on the modelling approach demonstrating how PRISM can be used to analyse and evaluate the reliability of the mobile agent control system learnt via the proposed algorithm. The results show that the path identified using the proposed integrated method yields the largest expected reward.</p

COMBINED ROBUST OPTIMAL DESIGN, PATH AND MOTION PLANNING FOR UNMANNED AERIAL VEHICLE SYSTEMS SUBJECT TO UNCERTAINTY

Unmanned system performance depends heavily on both how the system is planned to be operated and the design of the unmanned system, both of which can be heavily impacted by uncertainty. This dissertation presents methods for simultaneously optimizing both of these aspects of an unmanned system when subject to uncertainty. This simultaneous optimization under uncertainty of unmanned system design and planning is demonstrated in the context of optimizing the design and flight path of an unmanned aerial vehicle (UAV) subject to an unknown set of wind conditions. This dissertation explores optimizing the path of the UAV down to the level of determining flight trajectories accounting for the UAVs dynamics (motion planning) while simultaneously optimizing design. Uncertainty is considered from the robust (no probability distribution known) standpoint, with the capability to account for a general set of uncertain parameters that affects the UAVs performance. New methods are investigated for solving motion planning problems for UAVs, which are applied to the problem of mitigating the risk posed by UAVs flying over inhabited areas. A new approach to solving robust optimization problems is developed, which uses a combination of random sampling and worst case analysis. The new robust optimization approach is shown to efficiently solve robust optimization problems, even when existing robust optimization methods would fail. A new approach for robust optimal motion planning that considers a “black-box” uncertainty model is developed based off the new robust optimization approach. The new robust motion planning approach is shown to perform better under uncertainty than methods which do not use a “black-box” uncertainty model. A new method is developed for solving design and path planning optimization problems for unmanned systems with discrete (graph-based) path representations, which is then extended to work on motion planning problems. This design and motion planning approach is used within the new robust optimization approach to solve a robust design and motion planning optimization problem for a UAV. Results are presented comparing these methods against a design study using a DOE, which show that the proposed methods can be less computationally expensive than existing methods for design and motion planning problems

Control and Optimization for Aerospace Systems with Stochastic Disturbances, Uncertainties, and Constraints

The topic of this dissertation is the control and optimization of aerospace systems under the influence of stochastic disturbances, uncertainties, and subject to chance constraints. This problem is motivated by the uncertain operating environments of many aerospace systems, and the ever-present push to extract greater performance from these systems while maintaining safety. Explicitly accounting for the stochastic disturbances and uncertainties in the constrained control design confers the ability to assign the probability of constraint satisfaction depending on the level of risk that is deemed acceptable and allows for the possibility of theoretical constraint satisfaction guarantees. Along these lines, this dissertation presents novel contributions addressing four different problems: 1) chance-constrained path planning for small unmanned aerial vehicles in urban environments, 2) chance-constrained spacecraft relative motion planning in low-Earth orbit, 3) stochastic optimization of suborbital launch operations, and 4) nonlinear model predictive control for tracking near rectilinear halo orbits and a proposed stochastic extension. For the first problem, existing dynamic and informed rapidly-expanding random trees algorithms are combined with a novel quadratic programming-based collision detection algorithm to enable computationally efficient, chance-constrained path planning. For the second problem, a previously proposed constrained relative motion approach based on chained positively invariant sets is extended in this dissertation to the case where the spacecraft dynamics are controlled using output feedback on noisy measurements and are subject to stochastic disturbances. Connectivity between nodes is determined through the use of chance-constrained admissible sets, guaranteeing that constraints are met with a specified probability. For the third problem, a novel approach to suborbital launch operations is presented. It utilizes linear covariance propagation and stochastic clustering optimization to create an effective software-only method for decreasing the probability of a dangerous landing with no physical changes to the vehicle and only minimal changes to its flight controls software. For the fourth problem, the use of suboptimal nonlinear model predictive control (NMPC) coupled with low-thrust actuators is considered for station-keeping on near rectilinear halo orbits. The nonlinear optimization problems in NMPC are solved with time-distributed sequential quadratic programming techniques utilizing the FBstab algorithm. A stochastic extension for this problem is also proposed. The results are illustrated using detailed numerical simulations.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162992/1/awbe_1.pd

Motion planning and perception : integration on humanoid robots

This thesis starts by proposing a new framework for motion planning using stochastic maps, such as occupancy-grid maps. In autonomous robotics applications, the robot's map of the environment is typically constructed online, using techniques from SLAM. These methods can construct a dense map of the environment, or a sparse map that contains a set of identifiable landmarks. In this situation, path planning would be performed using the dense map, and the path would be executed in a sensor-based fashion, using feedback control to track the reference path based on sensor information regarding landmark position. Maximum-likelihood estimation techniques are used to model the sensing process as well as to estimate the most likely nominal path that will be followed by the robot during execution of the plan. The proposed approach is potentially a practical way to plan under the specific sorts of uncertainty confronted by a humanoid robot. The next chapter, presents methods for constructing free paths in dynamic environments. The chapter begins with a comprehensive review of past methods, ranging from modifying sampling-based methods for the dynamic obstacle problem, to methods that were specifically designed for this problem. The thesis proposes to adapt a method reported originally by Leven et al.. so that it can be used to plan paths for humanoid robots in dynamic environments. The basic idea of this method is to construct a mapping from voxels in a discretized representation of the workspace to vertices and arcs in a configuration space network built using sampling-based planning methods. When an obstacle intersects a voxel in the workspace, the corresponding nodes and arcs in the configuration space roadmap are marked as invalid. The part of the network that remains comprises the set of valid candidate paths. The specific approach described here extends previous work by imposing a two-level hierarchical structure on the representation of the workspace. The methods described in Chapters 2 and 3 essentially deal with low-dimensional problems (e.g., moving a bounding box). The reduction in dimensionality is essential, since the path planning problem confronted in these chapters is complicated by uncertainty and dynamic obstacles, respectively. Chapter 4 addresses the problem of planning the full motion of a humanoid robot (whole-body task planning). The approach presented here is essentially a four-step approach. First, multiple viable goal configurations are generated using a local task solver, and these are used in a classical path planning approach with one initial condition and multiple goals. This classical problem is solved using an RRT-based method. Once a path is found, optimization methods are applied to the goal posture. Finally, classic path optimization algorithms are applied to the solution path and posture optimization. The fifth chapter describes algorithms for building a representation of the environment using stereo vision as the sensing modality. Such algorithms are necessary components of the autonomous system proposed in the first chapter of the thesis. A simple occupancy-grid based method is proposed, in which each voxel in the grid is assigned a number indicating the probability that it is occupied. The representation is updated during execution based on values received from the sensing system. The sensor model used is a simple Gaussian observation model in which measured distance is assumed to be true distance plus additive Gaussian noise. Sequential Bayes updating is then used to incrementally update occupancy values as new measurements are received. Finally, chapter 6 provides some details about the overall system architecture, and in particular, about those components of the architecture that have been taken from existing software (and therefore, do not themselves represent contributions of the thesis). Several software systems are described, including GIK, WorldModelGrid3D, HppDynamicObstacle, and GenoM