[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83163-en":3,"doc-seo-83163-105":30,"detail-sidebar-cat-0-en-105":83},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83163,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Residual Conservative Model Predictive Path Integral Control","Residual-Conservative Model Predictive Path Integral Control (RC-MPPI) addresses model-plant mismatch in sampling-based MPC by adapting safety conservatism online. The framework couples three mechanisms: residual-dependent constraint tightening, adaptive safety-cost shaping, and residual-adaptive temperature relaxation. Temperature is increased when prediction quality degrades so rollout cost rankings are not overtrusted. Under Lipschitz dynamics and sub-Gaussian disturbances, probabilistic bounds are derived to show constraint-violation probability decreases monotonically with residual, supported by rollout-cost uncertainty analysis. The method is extended to a two-time-scale architecture with episodic refinement and validated via simulations on an LTI point-mass and a planar 2R manipulator.","Residual-Conservative Model Predictive Path Integral Control  \nHyung-Jin Yoon† and Hunmin Kim‡  \narXiv :2607 .06950v1 [ ee ss . SY] 8 Jul 2026  \nAbstract—Sampling-based model predictive control methods handle nonlinear dynamics and complex cost landscapes through Monte Carlo rollouts, yet typically employ fixed constraint penalties that do not adapt to model-plant mismatch. This paper proposes RC-MPPI, a sampling-based MPC framework that modulates safety conservatism online via three coupled mechanisms: residual-dependent constraint tightening, adaptive safety-cost shaping, and residual-adaptive temperature relaxation. The temperature adaptation reflects a key insight: when the model is inaccurate, rollout cost evaluations become unreliable, and raising temperature reduces overcommitment to apparent cost rankings. As model-plant mismatch increases, safety margins tighten and the MPPI temperature rises; as prediction fidelity improves, nominal MPPI behavior is recovered. Under Lipschitz dynamics and sub-Gaussian disturbances, we derive probabilistic bounds on constraint violation and establish that the joint effect of all three mechanisms monotonically reduces violation probability with growing residual. A rolloutcost uncertainty analysis further shows that mismatchinduced perturbations of MPPI importance weights scale proportionally to residual magnitude and inversely with temperature, providing theoretical justification for residualadaptive temperature relaxation under model-plant mismatch. We extend the method to a two-time-scale architecture with episodic model refinement. Simulations on an LTI point-mass and a planar 2R manipulator confirm systematic improvements in safety margin, success rate, and control efficiency over vanilla MPPI.  \nI. INTRODUCTION  \nLow-cost robotic and embedded control platforms frequently exhibit execution variability arising from actuation lag, saturation, unmodeled inner-loop dynamics, and limited sensing fidelity. When high-level planners rely on simplified or nominal actuator models, such effects induce modelplant mismatch that can compromise constraint satisfaction. In receding-horizon implementations, this mismatch is persistent and state-dependent rather than a one-time disturbance.  \nSampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI) control [1], [2], handle nonlinear dynamics and complex cost landscapes through Monte Carlo rollouts and importance weighting. However, standard formulations assume a fixed nominal model and employ static constraint penalties or barrier functions that do not adapt to model-plant mismatch. When  \n†H.-J. Yoon is with the Department of Mechanical and Nuclear Engineering, Tennessee Technological University, Cookeville, TN, USA.  \n‡H. Kim is with the School of Engineering, Department of Electrical and Computer Engineering, Mercer University, Macon, GA, USA.  \nThis work was supported by internal funding at Tennessee Technological University.  \nmodel-plant mismatch grows, fixed safety mechanisms may become insufficient.  \nThis paper addresses the problem of online conservatism adaptation under model-plant mismatch. Rather than performing real-time parameter identification or maintaining a full disturbance belief, we exploit the prediction–execution residual, the directly measurable discrepancy between predicted and realized state transitions, as a lightweight signal of model-plant mismatch, and embed it into the sampling-based MPC objective via three coupled adaptive mechanisms.  \nThe resulting method, Residual-Conservative MPPI (RC-MPPI), enforces safety through residual-dependent constraint tightening and amplified penalty scaling, while the MPPI temperature is relaxed in proportion to the observed prediction–execution residual. Standard MPPI treats temperature as a fixed exploration parameter; under model-plant mismatch, however, this conflates genuine cost differences with artifacts of an inaccurate model. RCMPPI instead","cbCaioLrXRNRWsXW","https://ap.wps.com/l/cbCaioLrXRNRWsXW","pdf",368484,3,1,9,"English","en",105,"# Introduction\n# Related Work","[{\"question\":\"What theoretical results support the proposed adaptation?\",\"answer\":\"Under Lipschitz dynamics and sub-Gaussian disturbances, the paper derives probabilistic bounds on constraint violation and shows the combined effect of the three mechanisms monotonically reduces violation probability as residual increases. A rollout-cost uncertainty analysis bounds mismatch-induced perturbations of MPPI importance weights and explains why temperature relaxation limits distortion of cost rankings.\"}]",1784185692,23,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"residual-conservative-model-predictive-path-integral-control","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/residual-conservative-model-predictive-path-integral-control/83163/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-21","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What theoretical results support the proposed adaptation?","Question",{"text":75,"@type":76},"Under Lipschitz dynamics and sub-Gaussian disturbances, the paper derives probabilistic bounds on constraint violation and shows the combined effect of the three mechanisms monotonically reduces violation probability as residual increases. 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