Pub Date : 2021-07-01DOI: 10.15607/rss.2021.xvii.081
Mengyu Fu, Oren Salzman, Ron Alterovitz
Medical steerable needles can move along 3D curvilinear trajectories to avoid anatomical obstacles and reach clinically significant targets inside the human body. Automating steerable needle procedures can enable physicians and patients to harness the full potential of steerable needles by maximally leveraging their steerability to safely and accurately reach targets for medical procedures such as biopsies and localized therapy delivery for cancer. For the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the motion planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable motion planner for steerable needles. We introduce the first motion planner for steerable needles that offers a guarantee, under clinically appropriate assumptions, that it will, in finite time, compute an exact, obstacle-avoiding motion plan to a specified target, or notify the user that no such plan exists. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. Compared to state-of-the-art steerable needle motion planners (none of which provide any completeness guarantees), we demonstrate that our new resolution-complete motion planner computes plans faster and with a higher success rate.
{"title":"Toward Certifiable Motion Planning for Medical Steerable Needles.","authors":"Mengyu Fu, Oren Salzman, Ron Alterovitz","doi":"10.15607/rss.2021.xvii.081","DOIUrl":"https://doi.org/10.15607/rss.2021.xvii.081","url":null,"abstract":"<p><p>Medical steerable needles can move along 3D curvilinear trajectories to avoid anatomical obstacles and reach clinically significant targets inside the human body. Automating steerable needle procedures can enable physicians and patients to harness the full potential of steerable needles by maximally leveraging their steerability to safely and accurately reach targets for medical procedures such as biopsies and localized therapy delivery for cancer. For the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the motion planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable motion planner for steerable needles. We introduce the first motion planner for steerable needles that offers a guarantee, under clinically appropriate assumptions, that it will, in finite time, compute an exact, obstacle-avoiding motion plan to a specified target, or notify the user that no such plan exists. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. Compared to state-of-the-art steerable needle motion planners (none of which provide any completeness guarantees), we demonstrate that our new resolution-complete motion planner computes plans faster and with a higher success rate.</p>","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"2021 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9612400/pdf/nihms-1786703.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40656353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-12DOI: 10.15607/rss.2020.xvi.069
D. Qiu, Yibiao Zhao, Chris L. Baker
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) model planning under world state uncertainty, but POMDPs with multimodal beliefs, continuous actions, and nonlinear dynamics suitable for robotics applications are challenging to solve. We present a dynamic programming algorithm for planning in the belief space over discrete latent states in POMDPs with continuous states, actions, observations, and nonlinear dynamics. Unlike prior belief space motion planning approaches which assume unimodal Gaussian uncertainty, our approach constructs a novel tree-structured representation of possible observations and multimodal belief space trajectories, and optimizes a contingency plan over this structure. We apply our method to problems with uncertainty over the reward or cost function (e.g., the configuration of goals or obstacles), uncertainty over the dynamics, and uncertainty about interactions, where other agents’ behavior is conditioned on latent intentions. Three experiments show that our algorithm outperforms strong baselines for planning under uncertainty, and results from an autonomous lane changing task demonstrate that our algorithm can synthesize robust interactive trajectories.
{"title":"Latent Belief Space Motion Planning under Cost, Dynamics, and Intent Uncertainty","authors":"D. Qiu, Yibiao Zhao, Chris L. Baker","doi":"10.15607/rss.2020.xvi.069","DOIUrl":"https://doi.org/10.15607/rss.2020.xvi.069","url":null,"abstract":"Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) model planning under world state uncertainty, but POMDPs with multimodal beliefs, continuous actions, and nonlinear dynamics suitable for robotics applications are challenging to solve. We present a dynamic programming algorithm for planning in the belief space over discrete latent states in POMDPs with continuous states, actions, observations, and nonlinear dynamics. Unlike prior belief space motion planning approaches which assume unimodal Gaussian uncertainty, our approach constructs a novel tree-structured representation of possible observations and multimodal belief space trajectories, and optimizes a contingency plan over this structure. We apply our method to problems with uncertainty over the reward or cost function (e.g., the configuration of goals or obstacles), uncertainty over the dynamics, and uncertainty about interactions, where other agents’ behavior is conditioned on latent intentions. Three experiments show that our algorithm outperforms strong baselines for planning under uncertainty, and results from an autonomous lane changing task demonstrate that our algorithm can synthesize robust interactive trajectories.","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72746908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.15607/RSS.2020.XVI.070
Utku Culha, Sinan O Demir, Sebastian Trimpe, Metin Sitti
Untethered small-scale soft robots have promising applications in minimally invasive surgery, targeted drug delivery, and bioengineering applications as they can access confined spaces in the human body. However, due to highly nonlinear soft continuum deformation kinematics, inherent stochastic variability during fabrication at the small scale, and lack of accurate models, the conventional control methods cannot be easily applied. Adaptivity of robot control is additionally crucial for medical operations, as operation environments show large variability, and robot materials may degrade or change over time, which would have deteriorating effects on the robot motion and task performance. Therefore, we propose using a probabilistic learning approach for millimeter-scale magnetic walking soft robots using Bayesian optimization (BO) and Gaussian processes (GPs). Our approach provides a data-efficient learning scheme to find controller parameters while optimizing the stride length performance of the walking soft millirobot robot within a small number of physical experiments. We demonstrate adaptation to fabrication variabilities in three different robots and to walking surfaces with different roughness. We also show an improvement in the learning performance by transferring the learning results of one robot to the others as prior information.
{"title":"Learning of Sub-optimal Gait Controllers for Magnetic Walking Soft Millirobots.","authors":"Utku Culha, Sinan O Demir, Sebastian Trimpe, Metin Sitti","doi":"10.15607/RSS.2020.XVI.070","DOIUrl":"https://doi.org/10.15607/RSS.2020.XVI.070","url":null,"abstract":"<p><p>Untethered small-scale soft robots have promising applications in minimally invasive surgery, targeted drug delivery, and bioengineering applications as they can access confined spaces in the human body. However, due to highly nonlinear soft continuum deformation kinematics, inherent stochastic variability during fabrication at the small scale, and lack of accurate models, the conventional control methods cannot be easily applied. Adaptivity of robot control is additionally crucial for medical operations, as operation environments show large variability, and robot materials may degrade or change over time, which would have deteriorating effects on the robot motion and task performance. Therefore, we propose using a probabilistic learning approach for millimeter-scale magnetic walking soft robots using Bayesian optimization (BO) and Gaussian processes (GPs). Our approach provides a data-efficient learning scheme to find controller parameters while optimizing the stride length performance of the walking soft millirobot robot within a small number of physical experiments. We demonstrate adaptation to fabrication variabilities in three different robots and to walking surfaces with different roughness. We also show an improvement in the learning performance by transferring the learning results of one robot to the others as prior information.</p>","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"2020 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7610446/pdf/EMS104319.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25536396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.15607/rss.2019.xv.057
Mengyu Fu, Alan Kuntz, Oren Salzman, Ron Alterovitz
Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans grows exponentially with the number of points of interest to inspect. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of successfully inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion planning roadmap using sampling-based algorithms, and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We demonstrate IRIS's efficacy on a simulated planar 5DOF manipulator inspection task and on a medical endoscopic inspection task for a continuum parallel surgical robot in cluttered anatomy segmented from patient CT data. We show that IRIS computes higher-quality inspection plans orders of magnitudes faster than a prior state-of-the-art method.
{"title":"Toward Asymptotically-Optimal Inspection Planning via Efficient Near-Optimal Graph Search.","authors":"Mengyu Fu, Alan Kuntz, Oren Salzman, Ron Alterovitz","doi":"10.15607/rss.2019.xv.057","DOIUrl":"https://doi.org/10.15607/rss.2019.xv.057","url":null,"abstract":"<p><p>Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans grows exponentially with the number of points of interest to inspect. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of successfully inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion planning roadmap using sampling-based algorithms, and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We demonstrate IRIS's efficacy on a simulated planar 5DOF manipulator inspection task and on a medical endoscopic inspection task for a continuum parallel surgical robot in cluttered anatomy segmented from patient CT data. We show that IRIS computes higher-quality inspection plans orders of magnitudes faster than a prior state-of-the-art method.</p>","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"2019 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7172008/pdf/nihms-1576709.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37857617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-26DOI: 10.15607/RSS.2018.XIV.044
Marc Toussaint, Kelsey R. Allen, Kevin A. Smith, J. Tenenbaum
We propose to formulate physical reasoning and manipulation planning as an optimization problem that integrates first order logic, which we call Logic-Geometric Programming.
我们建议将物理推理和操作规划作为集成一阶逻辑的优化问题,我们称之为逻辑几何规划。
{"title":"Differentiable Physics and Stable Modes for Tool-Use and Manipulation Planning","authors":"Marc Toussaint, Kelsey R. Allen, Kevin A. Smith, J. Tenenbaum","doi":"10.15607/RSS.2018.XIV.044","DOIUrl":"https://doi.org/10.15607/RSS.2018.XIV.044","url":null,"abstract":"We propose to formulate physical reasoning and manipulation planning as an optimization problem that integrates first order logic, which we call Logic-Geometric Programming.","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"67 5 1","pages":"6231-6235"},"PeriodicalIF":0.0,"publicationDate":"2018-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83431270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-18DOI: 10.15607/RSS.2016.XII.015
Fatemeh Zahra Saberifar, S. Ghasemlou, J. O’Kane, Dylan A. Shell
For a given robot and a given task, this paper addresses questions about which modifications may be made to the robot’s suite of sensors without impacting the robot’s behavior in completing its task. Though this is an important design-time question, few principled methods exist for providing a definitive answer in general. Utilizing and extending the language of combinatorial filters, this paper aims to fill that lacuna by introducing theoretical tools for reasoning about sensors and representations of sensors. It introduces new representations for sensors and filters, exploring the relationship between those elements and the specific information needed to perform a task. It then shows how these tools can be used to algorithmically answer questions about changes to a robot’s sensor suite. The paper substantially expands the expressiveness of combinatorial filters so that, where they were previously limited to quite simple sensors, our richer filters are able to reasonably model a much broader variety of real devices. We have implemented the proposed algorithms, and describe their application to an example instance involving a series of simplifications to the sensors of a specific, widely deployed mobile robot.
{"title":"Set-labelled filters and sensor transformations","authors":"Fatemeh Zahra Saberifar, S. Ghasemlou, J. O’Kane, Dylan A. Shell","doi":"10.15607/RSS.2016.XII.015","DOIUrl":"https://doi.org/10.15607/RSS.2016.XII.015","url":null,"abstract":"For a given robot and a given task, this paper addresses questions about which modifications may be made to the robot’s suite of sensors without impacting the robot’s behavior in completing its task. Though this is an important design-time question, few principled methods exist for providing a definitive answer in general. Utilizing and extending the language of combinatorial filters, this paper aims to fill that lacuna by introducing theoretical tools for reasoning about sensors and representations of sensors. It introduces new representations for sensors and filters, exploring the relationship between those elements and the specific information needed to perform a task. It then shows how these tools can be used to algorithmically answer questions about changes to a robot’s sensor suite. The paper substantially expands the expressiveness of combinatorial filters so that, where they were previously limited to quite simple sensors, our richer filters are able to reasonably model a much broader variety of real devices. We have implemented the proposed algorithms, and describe their application to an example instance involving a series of simplifications to the sensors of a specific, widely deployed mobile robot.","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91398153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-01DOI: 10.15607/RSS.2016.XII.018
Addisu Z Taddese, Piotr R Slawinski, Keith L Obstein, Pietro Valdastri
Magnetic field gradients have repeatedly been shown to be the most feasible mechanism for gastrointestinal capsule endoscope actuation. An inverse quartic magnetic force variation with distance results in large force gradients induced by small movements of a driving magnet; this necessitates robotic actuation of magnets to implement stable control of the device. A typical system consists of a serial robot with a permanent magnet at its end effector that actuates a capsule with an embedded permanent magnet. We present a tethered capsule system where a capsule with an embedded magnet is closed loop controlled in 2 degree-of-freedom in position and 2 degree-of-freedom in orientation. Capitalizing on the magnetic field of the external driving permanent magnet, the capsule is localized in 6-D allowing for both position and orientation feedback to be used in a control scheme. We developed a relationship between the serial robot's joint parameters and the magnetic force and torque that is exerted onto the capsule. Our methodology was validated both in a dynamic simulation environment where a custom plug-in for magnetic interaction was written, as well as on an experimental platform. The tethered capsule was demonstrated to follow desired trajectories in both position and orientation with accuracy that is acceptable for colonoscopy.
{"title":"Closed Loop Control of a Tethered Magnetic Capsule Endoscope.","authors":"Addisu Z Taddese, Piotr R Slawinski, Keith L Obstein, Pietro Valdastri","doi":"10.15607/RSS.2016.XII.018","DOIUrl":"https://doi.org/10.15607/RSS.2016.XII.018","url":null,"abstract":"<p><p>Magnetic field gradients have repeatedly been shown to be the most feasible mechanism for gastrointestinal capsule endoscope actuation. An inverse quartic magnetic force variation with distance results in large force gradients induced by small movements of a driving magnet; this necessitates robotic actuation of magnets to implement stable control of the device. A typical system consists of a serial robot with a permanent magnet at its end effector that actuates a capsule with an embedded permanent magnet. We present a tethered capsule system where a capsule with an embedded magnet is closed loop controlled in 2 degree-of-freedom in position and 2 degree-of-freedom in orientation. Capitalizing on the magnetic field of the external driving permanent magnet, the capsule is localized in 6-D allowing for both position and orientation feedback to be used in a control scheme. We developed a relationship between the serial robot's joint parameters and the magnetic force and torque that is exerted onto the capsule. Our methodology was validated both in a dynamic simulation environment where a custom plug-in for magnetic interaction was written, as well as on an experimental platform. The tethered capsule was demonstrated to follow desired trajectories in both position and orientation with accuracy that is acceptable for colonoscopy.</p>","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"2016 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5345944/pdf/nihms851663.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34806511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-01DOI: 10.15607/RSS.2016.XII.039
Yilun Zhou, George Konidaris
We present a framework for representing scenarios with complex object interactions, in which a robot cannot directly interact with the object it wishes to control, but must instead do so via intermediate objects. For example, a robot learning to drive a car can only indirectly change its pose, by rotating the steering wheel. We formalize such complex interactions as chains of Markov decision processes and show how they can be learned and used for control. We describe two systems in which a robot uses learning from demonstration to achieve indirect control: playing a computer game, and using a hot water dispenser to heat a cup of water.
{"title":"Representing and Learning Complex Object Interactions.","authors":"Yilun Zhou, George Konidaris","doi":"10.15607/RSS.2016.XII.039","DOIUrl":"https://doi.org/10.15607/RSS.2016.XII.039","url":null,"abstract":"<p><p>We present a framework for representing scenarios with complex object interactions, in which a robot cannot directly interact with the object it wishes to control, but must instead do so via intermediate objects. For example, a robot learning to drive a car can only indirectly change its pose, by rotating the steering wheel. We formalize such complex interactions as chains of Markov decision processes and show how they can be learned and used for control. We describe two systems in which a robot uses learning from demonstration to achieve indirect control: playing a computer game, and using a hot water dispenser to heat a cup of water.</p>","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"2016 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5459359/pdf/nihms859882.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35070620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-13DOI: 10.15607/RSS.2015.XI.005
Sanjiban Choudhury, S. Scherer, J. Bagnell
The performance of a state lattice motion planning algorithm depends critically on the resolution of the lattice to ensure a balance between solution quality and computation time. There is currently no theoretical basis for selecting the resolution because of its dependence on the robot dynamics and the distribution of obstacles. In this paper, we examine the problem of motion planning on a resolution constrained lattice for a robot with non-linear dynamics operating in an environment with randomly generated disc shaped obstacles sampled from a homogeneous Poisson process. We present a unified framework for computing explicit solutions to two problems i) the critical planning resolution which guarantees the existence of an infinite collision free trajectory in the search graph ii) the critical speed limit which guarantees infinite collision free motion. In contrast to techniques used by Karaman and Frazzoli [11], we use a novel approach that maps the problem to parameters of directed asymmetric hexagonal lattice bond percolation. Since standard percolation theory offers no results for this lattice, we map the lattice to an infinite absorbing Markov chain and use results pertaining to its survival to obtain bounds on the parameters. As a result, we are able to derive theoretical expressions that relate the non-linear dynamics of a robot, the resolution of the search graph and the density of the Poisson process. We validate the theoretical bounds using Monte-Carlo simulations for single integrator and curvature constrained systems and are able to validate the previous results presented by Karaman and Frazzoli [11] independently using the novel connections introduced in this paper.
{"title":"Theoretical Limits of Speed and Resolution for Kinodynamic Planning in a Poisson Forest","authors":"Sanjiban Choudhury, S. Scherer, J. Bagnell","doi":"10.15607/RSS.2015.XI.005","DOIUrl":"https://doi.org/10.15607/RSS.2015.XI.005","url":null,"abstract":"The performance of a state lattice motion planning algorithm depends critically on the resolution of the lattice to ensure a balance between solution quality and computation time. There is currently no theoretical basis for selecting the resolution because of its dependence on the robot dynamics and the distribution of obstacles. In this paper, we examine the problem of motion planning on a resolution constrained lattice for a robot with non-linear dynamics operating in an environment with randomly generated disc shaped obstacles sampled from a homogeneous Poisson process. We present a unified framework for computing explicit solutions to two problems i) the critical planning resolution which guarantees the existence of an infinite collision free trajectory in the search graph ii) the critical speed limit which guarantees infinite collision free motion. In contrast to techniques used by Karaman and Frazzoli [11], we use a novel approach that maps the problem to parameters of directed asymmetric hexagonal lattice bond percolation. Since standard percolation theory offers no results for this lattice, we map the lattice to an infinite absorbing Markov chain and use results pertaining to its survival to obtain bounds on the parameters. As a result, we are able to derive theoretical expressions that relate the non-linear dynamics of a robot, the resolution of the search graph and the density of the Poisson process. We validate the theoretical bounds using Monte-Carlo simulations for single integrator and curvature constrained systems and are able to validate the previous results presented by Karaman and Frazzoli [11] independently using the novel connections introduced in this paper.","PeriodicalId":87357,"journal":{"name":"Robotics science and systems : online proceedings","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91386620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}