Generation of Probabilistically Optimal Paths for Nonholonomic Needle Insertion

2016 ◽  
Author(s):  
Jianping Lin ◽  
Wooram Park
Keyword(s):  
Cost Function ◽  
Optimal Path ◽  
Target Position ◽  
Nonholonomic Constraints ◽  
Needle Insertion ◽  
Initial State ◽  
Goal State ◽  
Medical Needles ◽  
The Cost ◽  
Planning Problems

Rapidly-exploring Random Tree (RRT) is a sampling-based algorithm which is designed for path planning problems. It is efficient to handle high-dimensional configuration space (C-space) and nonholonomic constraints. Under the nonholonomic constraints, the RRT can generate paths between an initial state and a goal state while avoiding obstacles. Since this framework assumes that a system is deterministic, more improvement should be added when the method is applied to a system with uncertainty. In robotic systems with motion uncertainty, probability for successful targeting and obstacle avoidance are more suitable measurement than the deterministic distance between the robot system and the target position. In this paper, the probabilistic targeting error is defined as a root-mean-square (RMS) distance between the system to the desired target. The proximity of the obstacle to the system is also defined as an averaged distance of obstacles to the robotic system. Then, we consider a cost function that is a sum of the targeting error and the obstacle proximity. By numerically minimizing the cost, we can obtain the optimal path. In this paper, a method for efficient evaluation and minimization of this cost function is proposed and the proposed method is applied to nonholonomic flexible medical needles for performance tests.

scholarly journals D* lite algorithm based path planning of mobile robot in static Environment

2012 ◽  
pp. 286-290
Author(s):  
Pradipta kumar Das ◽  
S .N. Patro ◽  
C. N. Panda ◽  
Bunil Balabantaray
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Cost Function ◽  
Shortest Path ◽  
Target Position ◽  
Initial Position ◽  
Distance Metric ◽  
Unknown Environment ◽  
Feasible Path ◽  
The Cost

In this paper, we study the path planning for khepera II mobile robot in an unknown environment. The well known heuristic D* lite algorithm is implemented to make the mobile robot navigate through static obstacles and find the shortest path from an initial position to a target position by avoiding the obstacles. and to perform efficient re-planning during exploration. The proposed path finding strategy is designed in a grid-map form of an unknown environment with static unknown obstacles. The robot moves within the unknown environment by sensing and avoiding the obstacles coming across its way towards the target. When the mission is executed, it is necessary to plan an optimal or feasible path for itself avoiding obstructions in its way and minimizing a cost such as time, energy, and distance. In our study we have considered the distance metric as the cost function.

scholarly journals Path Planning of Mobile Robot in Unknown Environment

2010 ◽  
pp. 122-127
Author(s):  
Pradipta kumar Das ◽  
Romesh Laishram ◽  
Amit Konar
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Cost Function ◽  
Shortest Path ◽  
Target Position ◽  
Initial Position ◽  
A Algorithm ◽  
Unknown Environment ◽  
Feasible Path ◽  
The Cost

In this paper, we study the online path planning for khepera II mobile robot in an unknown environment. The well known heuristic A* algorithm is implemented to make the mobile robot navigate through static obstacles and find the shortest path from an initial position to a target position by avoiding the obstacles. The proposed path finding strategy is designed in a grid-map form of an unknown environment with static unknown obstacles. When the mission is executed, it is necessary to plan an optimal or feasible path for itself avoiding obstructions in its way and minimizing a cost such as time, energy, and distance. In our study we have considered the distance and time metric as the cost function.

scholarly journals Optimal path planning for surveillance with temporal-logic constraints

2011 ◽  
Vol 30 (14) ◽  
pp. 1695-1708 ◽  
Author(s):  
Stephen L Smith ◽  
Jana Tůmová ◽  
Calin Belta ◽  
Daniela Rus
Keyword(s):  
Data Collection ◽  
Cost Function ◽  
Temporal Logic ◽  
Optimal Path ◽  
Data Gathering ◽  
Graph Algorithm ◽  
Complex Data ◽  
High Level ◽  
The Cost ◽  
Robot Path

In this paper we present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path that minimizes the cost function. The problem is motivated by applications in robotic monitoring and data-gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data-collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal-logic specification. We then present a graph algorithm that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.

A rewriting framework and logic for activities subject to regulations

2015 ◽  
Vol 27 (3) ◽  
pp. 332-375 ◽  
Author(s):  
MAX KANOVICH ◽  
TAJANA BAN KIRIGIN ◽  
VIVEK NIGAM ◽  
ANDRE SCEDROV ◽  
CAROLYN TALCOTT ◽  
...  
Keyword(s):  
Human Error ◽  
Linear Logic ◽  
Formal Semantics ◽  
Time Constraints ◽  
Negative Consequences ◽  
Initial State ◽  
Goal State ◽  
Model Based ◽  
Compliance Problem ◽  
Planning Problems

Activities such as clinical investigations (CIs) or financial processes are subject to regulations to ensure quality of results and avoid negative consequences. Regulations may be imposed by multiple governmental agencies as well as by institutional policies and protocols. Due to the complexity of both regulations and activities, there is great potential for violation due to human error, misunderstanding, or even intent. Executable formal models of regulations, protocols and activities can form the foundation for automated assistants to aid planning, monitoring and compliance checking. We propose a model based on multiset rewriting where time is discrete and is specified by timestamps attached to facts. Actions, as well as initial, goal and critical states may be constrained by means of relative time constraints. Moreover, actions may have non-deterministic effects, i.e. they may have different outcomes whenever applied. We present a formal semantics of our model based on focused proofs of linear logic with definitions. We also determine the computational complexity of various planning problems. Plan compliance problem, for example, is the problem of finding a plan that leads from an initial state to a desired goal state without reaching any undesired critical state. We consider all actions to be balanced, i.e. their pre- and post-conditions have the same number of facts. Under this assumption on actions, we show that the plan compliance problem is PSPACE-complete when all actions have only deterministic effects and is EXPTIME-complete when actions may have non-deterministic effects. Finally, we show that the restrictions on the form of actions and time constraints taken in the specification of our model are necessary for decidability of the planning problems.

Composition of Optimal Service Workflows with Quality-of-Service Enabled Multi-Criteria Uniform Cost Search Algorithm

2012 ◽  
Vol 3 (3) ◽  
pp. 1-25
Author(s):  
Jaina Sangtani ◽  
Gursel Serpen
Keyword(s):  
Service Oriented Architecture ◽  
Search Algorithm ◽  
Optimal Path ◽  
Computational Cost ◽  
Initial State ◽  
Goal State ◽  
Composition Problem ◽  
Service Oriented ◽  
Workflow Composition

This paper proposes a search-based method to partly automate the workflow composition, including the planning and execution stages, with web services in a service-oriented architecture. The proposed methodology models the workflow composition problem as a directed and weighted graph, henceforth called the service-oriented architecture graph, where vertices are associated with the degree of completion of the overall task at hand and edges represent service executions. Edge weights are formulated based on the quality of services as defined by the user. A uniform cost search algorithm is adapted and applied to identify the optimal path based on user input, which constitutes an ordered sequence of service executions, from a given initial state to a user-defined goal state. The proposed approach for service oriented workflow composition was applied to an information-technology domain problem to demonstrate its utility through a simulation study. Simulation results indicated that the proposed methodology is feasible and optimal solutions can be computed within reasonable computational cost bounds.

scholarly journals OPP approach for multi degree of freedom robotic arm Based on Kinematics and Dynamics of Robot

2015 ◽  
Vol 4 (4) ◽  
pp. 284
Author(s):  
Praneet Dutta ◽  
Rashmi Ranjan Das ◽  
Rupali Mathur ◽  
Deepika Rani Sona
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Minimum Principle ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Minimum Cost ◽  
Simulation Software ◽  
Degree Of Freedom ◽  
The Cost ◽  
Joint Velocity

This paper deals with the trajectory and path generation of the industrial manipulator. The trajectory is obtained using the equations of motion and also the optimal path planning (OPP) approach under kinodynamic constraints. The optimal control problem is defined for the minimum cost function and to obtain the necessary conditions. Here we have used pontrygain’s minimum principle to obtain the limiting value of joint angle and also  the joint velocity and torque. In this paper we have used the “Two degree of freedom (DOF) manipulator” for analysis and designing the optimal control for multi link and multi degree of freedom manipulator. For analysis purposes,  simulation software has been used to formulate the trajectory and minimize the cost function involved.

scholarly journals Effective grounding for hybrid planning problems represented in PDDL+

2021 ◽  
Vol 36 ◽  
Author(s):  
Enrico Scala ◽  
Mauro Vallati
Keyword(s):  
Real World ◽  
Automated Planning ◽  
Search Space ◽  
Language Models ◽  
State Variables ◽  
Initial State ◽  
Discrete State ◽  
Goal State ◽  
Search Spaces ◽  
Planning Problems

Abstract Automated planning is the field of Artificial Intelligence (AI) that focuses on identifying sequences of actions allowing to reach a goal state from a given initial state. The need of using such techniques in real-world applications has brought popular languages for expressing automated planning problems to provide direct support for continuous and discrete state variables, along with changes that can be either instantaneous or durative. PDDL+ (Planning Domain Definition Language +) models support the encoding of such representations, but the resulting planning problems are notoriously difficult for AI planners to cope with due to non-linear dependencies arising from the variables and infinite search spaces. This difficulty is exacerbated by the potentially huge fully ground representations used by modern planners in order to effectively explore the search space, which can make some problems impossible to tackle. This paper investigates two grounding techniques for PDDL+ problems, both aimed at reducing the size of the full ground representation by reasoning over the lifted, more abstract problem structure. The first method extends the simple mechanism of invariant analysis to limit the groundings of operators upfront. The second method proposes to tackle the grounding process through a PDDL+ to classical planning abstraction; this allows us to leverage the amount of research done in the classical planning area. Our empirical analysis studies the effect of these novel approaches over both real-world hybrid applications and synthetic PDDL+ problems took from standard benchmarks of the planning community; our results reveal that not only the techniques improve the running time of previous grounding mechanisms but also let the planner extend the reach to problems that were not solvable before.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Sorting permutations by fragmentation-weighted operations

2020 ◽  
Vol 18 (02) ◽  
pp. 2050006 ◽  
Author(s):  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Approximation Algorithms ◽  
Computational Biology ◽  
Cost Function ◽  
Traditional Approach ◽  
Upper Bounds ◽  
Evolutionary Distance ◽  
Lower And Upper Bounds ◽  
Approximation Factor ◽  
New Type ◽  
The Cost

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species’ genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

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