[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84668-en":3,"doc-seo-84668-105":29,"detail-sidebar-cat-0-en-105":91},{"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":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84668,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",6,"Technology","RCOA Extension and Applications","Relaxed Convex Obstacle Avoidance (RCOA) enables a fully convex optimal control problem for obstacle avoidance, supported by convergence analysis that guarantees obstacle-avoidance efficacy even when obstacles lie beyond the controller’s prediction horizon. The work extends RCOA to three-dimensional environments and applies it to UAV navigation. It further incorporates vehicle geometries to support collision avoidance between 3D objects rather than point masses. Numerical simulations show real-time feasibility for NMPC at over 30 Hz.","RCOA Extension and Applications  \nRicardo Tapia, Iman Soltani  \narXiv :2607 .02797v1 [ ee ss . SY] 2 Jul 2026  \nAbstract—The Relaxed Convex Obstacle Avoidance (RCOA) formulation is the first approach to enable a fully convex optimal control problem (OCP) for obstacle avoidance. Convergence analysis of RCOA yields an analytical framework that defines a unique characteristic: the ability to maintain obstacle avoidance (OA) efficacy even when obstacles reside beyond the controller’s prediction horizon. In this paper, RCOA is extended to three-dimensional environments and apply it to Unmanned Aerial Vehicle (UAV) navigation. Furthermore, the formulation is enhanced to incorporate vehicle geometries, moving beyond point-mass representations to enable collision avoidance between 3D objects. Numerical simulations demonstrate that RCOA provides computational performance on par or exceeding stateof-the-art methods. Notably, RCOA is demonstrated to enable a Nonlinear Model Predictive Controller (NMPC) to execute aggressive maneuvers through narrow passages with reduced prediction horizons, ensuring real-time feasibility at frequencies exceeding 30 Hz.  \nI. INTRODUCTION  \nThe proliferation of Unmanned Aerial Vehicles (UAVs) in highly constrained, unstructured environments ranging from urban air mobility and autonomous delivery to search and rescue operations in collapsed structures, has intensified the demand for robust local path planning. In these scenarios, autonomy requires not only navigating unforeseen environmental changes and dynamic obstacles but doing so while pushing the vehicle to its dynamic limits. Local planners must generate trajectories that are strictly collision-free, respect high-order nonlinear vehicle dynamics, and satisfy external constraints such as actuator saturation or wind disturbances [1] .  \nExisting methodologies are broadly categorized into nonoptimization and optimization-based approaches. Classic nonoptimization methods, such as Artificial Potential Fields (APF)  \n[2], Hybrid A*, and the Dynamic Window Approach (DWA)  \n[3], are computationally efficient but often suffer from local minima or a lack of dynamic consistency. Recent efforts have attempted to mitigate these issues by hybridizing samplingbased methods like RRT with DWA or Reinforcement Learning [4], [5] . However, these multi-component frameworks often increase architectural complexity without addressing the underlying limitations of the individual algorithms. Samplingbased methods, in particular, struggle with high-dimensional differential constraints, often requiring the solution of complex Boundary Value Problems (BVP) or excessive linearization to maintain accuracy between nodes [6] .  \nRicardo Tapia is with the Laboratory for AI, Robotics and Automation, University of California at Davis, Davis, CA 95616 USA. Email: [ricardo.tapia.m@proton.me](ricardo.tapia.m@proton.me).  \nIman Soltani (Corresponding Author, Lab PI) is with the Laboratory for AI, Robotics and Automation, University of California at Davis, Davis, CA 95616 USA. Email: [isoltani@ucdavis.edu](isoltani@ucdavis.edu)  \nAuthor contributions: Ricardo Tapia conceived the project, designed and carried out the simulations, performed the analysis, and wrote the manuscript. Lab PI Iman Soltani sponsored this work in part.  \nOptimization-based methods, specifically Model Predictive Control and Nonlinear MPC (NMPC), inherently integrate dynamics and constraints. However, their real-time application is often hindered by two factors: (i) the nonconvexity of vehicle dynamics and (ii) the computational burden of obstacle avoidance constraints. While convex OCPs enjoy fast convergence, nonconvex formulations for obstacle avoidance typically require sequential quadratic programming (SQP) or successive convexification programming (SSCP) to remain tractable. A significant limitation of standard (N)MPC is its dependence on the prediction horizon; if an obstacle is outside this horizon, the control","cbCaiaVa6K52tyQX","https://ap.wps.com/l/cbCaiaVa6K52tyQX","pdf",608232,1,11,"English","en",105,"# Introduction\n## UAV local path planning in constrained environments\n## Existing obstacle-avoidance methods and limitations\n## MPC/NMPC challenges: horizon dependence and nonconvexity\n## Point-mass modeling limitations and geometry-aware collision avoidance","[{\"question\":\"What problem does RCOA address in obstacle avoidance optimal control?\",\"answer\":\"RCOA reformulates obstacle avoidance as a fully convex optimal control problem, providing a convergence-based framework that maintains avoidance efficacy even when obstacles are outside the prediction horizon.\"},{\"question\":\"How is RCOA extended beyond the original setting?\",\"answer\":\"The method is extended to three-dimensional environments for UAV navigation and enhanced to incorporate vehicle geometries, enabling collision avoidance between 3D objects instead of point-mass approximations.\"},{\"question\":\"Why does standard NMPC struggle in fast, cluttered flight?\",\"answer\":\"Standard NMPC becomes “blind” when obstacles are outside the prediction horizon, and increasing the horizon raises computational cost and can break real-time feasibility; shortening the horizon makes the controller “myopic,” often leading to collisions under hard spatial constraints.\"}]",1784197569,28,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"rcoa-extension-and-applications","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/technology/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/rcoa-extension-and-applications/84668/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does RCOA address in obstacle avoidance optimal control?","Question",{"text":75,"@type":76},"RCOA reformulates obstacle avoidance as a fully convex optimal control problem, providing a convergence-based framework that maintains avoidance efficacy even when obstacles are outside the prediction horizon.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is RCOA extended beyond the original setting?",{"text":80,"@type":76},"The method is extended to three-dimensional environments for UAV navigation and enhanced to incorporate vehicle geometries, enabling collision avoidance between 3D objects instead of point-mass approximations.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does standard NMPC struggle in fast, cluttered flight?",{"text":84,"@type":76},"Standard NMPC becomes “blind” when obstacles are outside the prediction horizon, and increasing the horizon raises computational cost and can break real-time feasibility; 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