[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84920-en":3,"doc-seo-84920-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},84920,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Clustering-Embedded Model Predictive Path Integral Control","Model Predictive Path Integral (MPPI) motion planning uses stochastic rollouts with importance-weighted updates, but averaging-induced failure can emerge in cluttered, non-convex environments where feasible modes are incompatible. The paper introduces Clustering-Embedded MPPI (CEMPPI), which replaces standard averaging with pruning and density clustering of feasible trajectories. DBSCAN, driven by a geometric direction feature from collision-derived reference points, isolates avoidance modes. Cluster selection is cost-optimal for static scenes and obstacle-flux-opposed for dynamic scenes. JAX GPU-accelerated 2-D simulations and Isaac Gym tests with a UR5e manipulator reduce time-to-goal and shorten end-effector paths.","Clustering-Embedded Model Predictive Path Integral Control: Avoiding Averaging-Induced Failure and Enabling Efficient Cluster Selection for  \nDynamic Obstacles  \nZidong Liu 1 , Kaixin Chang 1 and Xu Chen†, 1  \narXiv :2607 .06499v 1 [ cs .RO] 7 Jul 2026  \nAbstract—With the widespread availability of parallel computing hardware, sampling-based motion planning methods such as Model Predictive Path Integral (MPPI) control have become increasingly powerful for complex nonlinear systems in non-smooth task spaces. However, the sampling and forwardsimulation pipeline in MPPI suffers from averaging-induced failure in cluttered environments, where the importanceweighted update averages incompatible rollouts and leads to hesitation or even collision when an obstacle lies directly ahead. This paper proposes Clustering-Embedded MPPI (CEMPPI), a framework that architecturally resolves the averaginginduced failures inherent in standard MPPI within non-convex environments. Rather than simply mitigating interference, CEMPPI redefines the control law by integrating a high-fidelity pruning and clustering stage. By leveraging density-based spatial clustering of applications with noise (DBSCAN) alongside a novel geometric direction feature that is extracted from collision-derived reference points, the system isolates feasible trajectory modes from the noise of infeasible rollouts. This is paired with an intelligent selection logic that optimizes for minimum cost in static scenes while actively steering opposite to obstacle flux in dynamic environments. Experiments in 2-D JAX-accelerated simulations show that CE-MPPI alleviates obstacle-front hesitation and avoids persistent coupling with moving obstacles in dynamic scenes. In particular, real-world tests on a 6-DoF UR5e manipulator with CUDA-parallel rolloutsin Isaac Gym achieve a 48% reduction in time-to-goal and a 12% shorter end-effector path.  \nI. INTRODUCTION  \nWith the rapid growth of computing hardware, samplingbased motion planning methods [1], [2] such as Model Predictive Path Integral (MPPI) control [3] have become increasingly popular for real-time robotic motion planning. MPPI iteratively generates stochastic rollouts, performs forward simulation, evaluates trajectory costs, and applies a path-integral weighted update to refine the control sequence. Compared to traditional gradient-based MPC [4], MPPI does not require the cost function to be differentiable, making it convenient to deploy with nonlinear dynamics and complex, non-smooth objectives [5] . Moreover, unlike learningbased approaches such as reinforcement learning [6] that typically rely on extensive offline training, sampling-based motion planning operates as a fully online planner and  \n*This work was supported in part by an Amazon-UW Science Hub Gift Award. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the sponsoring organization.  \n† : corresponding author.  \n1Department of Mechanical Engineering, University of Washington, Seattle, WA, USA. {liuzd, kxc118, [chx](chx}@uw.edu)[}](chx}@uw.edu)[@uw.edu](chx}@uw.edu)  \ncan further benefit from GPU-accelerated parallel rollout computation [7] for real-time performance.  \nThe performance of sampling-based motion planning hinges on the sampling number and the diversity of rollouts [8] . For example for MPPI, at each replanning step, the algorithm samples control sequences by injecting stochastic perturbations (typically Gaussian noise) around a nominal control sequence and then applies an importance-weighted update. However, the weighted averaging mechanism can be problematic in cluttered environments with multi-modal feasible solutions [9] . As illustrated in Fig. 1, even when colliding rollouts receive negligible weights, importanceweighted averaging of left- and right-passing rollouts can produce a control update toward the obstacle, causing hesit","cbCaio5k0S8ipDnK","https://ap.wps.com/l/cbCaio5k0S8ipDnK","pdf",4334208,1,"English","en",105,"# Introduction\n## Averaging-induced failure in MPPI\n## Clustering-Embedded MPPI (CE-MPPI) approach\n## Validation setup and results","[{\"question\":\"What problem does the paper address in standard MPPI?\",\"answer\":\"Standard MPPI can suffer averaging-induced failure: importance-weighted averaging across incompatible feasible modes may steer the control update toward an obstacle, causing hesitation or even collision.\"},{\"question\":\"How does CEMPPI avoid averaging-induced failure?\",\"answer\":\"CEMPPI prunes colliding rollouts, then clusters remaining feasible trajectories using DBSCAN with a geometric direction feature derived from collision-related reference points, and updates the nominal control using only the selected cluster.\"},{\"question\":\"How is cluster selection different for static versus dynamic obstacles?\",\"answer\":\"For static obstacles, CEMPPI selects the cluster with the minimum average cost. For dynamic obstacles, it estimates obstacle motion and selects the cluster whose motion is most opposite to the obstacle’s flux using a dot-product criterion.\"}]",1784199345,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"clustering-embedded-model-predictive-path-integral-control","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/clustering-embedded-model-predictive-path-integral-control/84920/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does the paper address in standard MPPI?","Question",{"text":74,"@type":75},"Standard MPPI can suffer averaging-induced failure: importance-weighted averaging across incompatible feasible modes may steer the control update toward an obstacle, causing hesitation or even collision.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does CEMPPI avoid averaging-induced failure?",{"text":79,"@type":75},"CEMPPI prunes colliding rollouts, then clusters remaining feasible trajectories using DBSCAN with a geometric direction feature derived from collision-related reference points, and updates the nominal control using only the selected cluster.",{"name":81,"@type":72,"acceptedAnswer":82},"How is cluster selection different for static versus dynamic obstacles?",{"text":83,"@type":75},"For static obstacles, CEMPPI selects the cluster with the minimum average cost. For dynamic obstacles, it estimates obstacle motion and selects the cluster whose motion is most opposite to the obstacle’s flux using a dot-product criterion.","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,126,129,133],{"id":20,"doc_module":4,"doc_module_name":44,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":45,"doc_module":4,"doc_module_name":44,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":44,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":44,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":44,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":44,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":44,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":44,"category_name":124,"show_sort_weight":27,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":27,"doc_module":4,"doc_module_name":44,"category_name":127,"show_sort_weight":27,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":44,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":44,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]