[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84506-en":3,"doc-seo-84506-105":29,"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":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},84506,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Series-Elastic Instantiation","Safe rehabilitation is formulated as an interaction-dynamics control task where a robot must track a prescribed motion while rejecting disturbances from patient spasm, voluntary effort, actuator compliance, and model mismatch. The work instantiates a predictive interaction-dynamics framework for a series-elastic-actuated knee: SEA feedforward yields a constant-coefficient double integrator, and dynamic-residual spring-deflection measurements enable disturbance estimation. A steady-state target cancels the estimated disturbance within a finite-horizon QP under ROM, torque, and velocity constraints. Matched-impedance evaluation shows large error reduction versus classical impedance and non-estimating MPC.","Interaction Dynamics MPC for Knee Rehabilitation Exoskeletons: A Series-Elastic Instantiation  \nYongyan Cao and Jinshan Tang  \narXiv :2606 . 13485v2 [ ee ss . SY] 11 Jul 2026  \nAbstract—Safe rehabilitation is an interaction-dynamics problem: the controller must regulate a prescribed motion while absorbing involuntary spasm, voluntary effort, actuator compliance, and model mismatch as interaction disturbances. This paper instantiates the predictive interaction-dynamics framework of the base pHRI formulation on a series-elastic-actuated knee joint. SEA feedforward reduces the gravity-compensated knee to the same constant-coefficient scalar double integrator used in the base framework, while a dynamic-residual measurement from spring deflection supplies an interaction-disturbance observation. A steady-state target converts the estimated disturbance into a cancelling input, and a finite-horizon quadratic program regulates deviations from that target under range-of-motion, torque, and velocity constraints. The evaluation is stiffnessand damping-matched so improvements cannot be attributed to higher impedance. Under a motion-opposing 15Nm step, classical impedance and MPC without estimation produce about 500mrad steady-state error, whereas Kalman-augmented interaction MPC reduces this to 1. 17mrad at 100 Hz and 0.70mrad at 500 Hz; the 500 Hz peak is 7.27mrad. In 30 randomized trials, the 95th-percentile peak is 21.57mrad. Bounded Assist-asNeeded scheduling, a corrective-channel energy tank, inequalityconstrained OSQP stress cases, direct MuJoCo execution, and a posture-clamped MyoSuite knee-slice run are implemented. The results support the SEA-knee instantiation of the interactiondynamics framework while separating it from clinical intent recognition, full-system passivity, safety certification, hardware trials, and free-standing multi-joint validation.  \nIndex Terms—Interaction dynamics, knee rehabilitation, exoskeleton, model predictive control, offset-free MPC, Kalman filter, series elastic actuator, disturbance estimation, impedance control, MuJoCo.  \nI. INTRODUCTION  \nPHYSICAL rehabilitation is not only a trajectory-tracking  \nproblem. It is an interaction-dynamics problem in which the robot, the actuator, the patient limb, involuntary spasm, voluntary effort, and unmodeled compliance jointly determine the interface motion. The base pHRI framework [19] shows that, after appropriate feedforward, such interaction dynamics can be represented by a constant-coefficient double integrator with an estimated persistent disturbance. This paper asks whether that representation survives a rehabilitation-specific actuator and sensing stack: a series-elastic-actuated (SEA) knee exoskeleton.  \nThe knee setting is a useful stress case for the framework. Fixed-gain impedance control is transparent and clinically familiar, but a constant interaction disturbance produces the  \nManuscript submitted June 2026 .  \nY. Cao is with Voryx Robotics, and J. Tang is with George Mason University, Dept. of Health Administration and Policy. Corresponding author:  \nY. Cao (e-mail: [yongyancao@gmail.com](yongyancao@gmail.com)).  \nequilibrium error e∞ = τh /K. A 15Nm disturbance at K = 30Nm/rad produces 500mrad (28 .6◦ ) error. Increasing stiffness reduces this error but changes the physical interaction and can increase contact load on a recovering joint. A fair evaluation of prediction or disturbance estimation must therefore match the realized stiffness and damping rather than allowing a predictive controller to win by becoming stiffer.  \nWithin the interaction-dynamics view, different robots differ mainly in the recovery map from physical coordinates to the normalized residual model. A rigid manipulator uses computed torque or operational-space feedforward; a hydraulic or cable device uses pressure or tension compensation; a quasi-directdrive joint uses current-based torque compensation. For the SEA knee, the inner force loop and gravity/inertia/damping feed","cbCailIched9gRyf","https://ap.wps.com/l/cbCailIched9gRyf","pdf",455591,1,9,"English","en",105,"# Introduction\n# Related Work\n## Interaction Dynamics, Impedance, and Predictive Control","[{\"question\":\"Why is the evaluation designed with matched impedance at 100 Hz and 500 Hz?\",\"answer\":\"To ensure improvements are attributable to disturbance estimation and target handling rather than simply increasing impedance stiffness.\"}]",1784196184,23,{"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":78,"head_meta":80,"extra_data":82,"updated_unix":27},"interaction-dynamics-mpc-for-knee-rehabilitation-exoskeletons-a-series-elastic-instantiation","",{"@graph":35,"@context":77},[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/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/interaction-dynamics-mpc-for-knee-rehabilitation-exoskeletons-a-series-elastic-instantiation/84506/",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],{"name":72,"@type":73,"acceptedAnswer":74},"Why is the evaluation designed with matched impedance at 100 Hz and 500 Hz?","Question",{"text":75,"@type":76},"To ensure improvements are attributable to disturbance estimation and target handling rather than simply increasing impedance stiffness.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,119,122,126],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]