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Learning Varying Physical Therapist-Patient Interactions for Robot-mediated Upper Limb Task-Specific Training

Jia Quan Loh, Vincent Crocher, Marlena Klaic, Denny Oetomo, Ying Tan

arXiv:2608.15995v1cs.ROcs.LG

TL;DR

Robotic task-specific training must adapt therapist-like physical interactions across dynamic task conditions, but evidence for such personalised interaction modelling remains limited. This paper learns therapist-applied torques from patient kinematics using TPGMM and compares it with a look-up table; both methods generalise to unseen variations, with TPGMM slightly outperforming the benchmark and performance improving with task complexity.

  • Problem

    Robots delivering task-specific training must adapt therapist-like physical interactions across dynamic environments with varying task conditions.

  • Method

    A TPGMM-based learning-from-demonstration framework models patient kinematics and therapist-applied torques, generalising interactions across task variations against a look-up-table benchmark.

  • Results

    Both methods slightly deviated from therapist-behaviour variability in unseen variations, while their generalisation performance improved significantly as task complexity increased; TPGMM had a small significant advantage.

  • Takeaways & Limitations

    The findings suggest TPGMM and look-up-table methods may suit robot-assisted task-specific training across varying task conditions.

  • Takeaways & Limitations

    The study cannot claim direct applicability to neuro-rehabilitation because interactions were constrained and evaluated offline without validating real-time human-in-the-loop efficacy.

Abstract

from arXiv · show

Upper extremity motor function recovery is positively linked to Task-Specific Training (TST) and sufficient therapy dosage. Rehabilitation robots can increase TST dosage via controlled, repetitive treatment and free therapists to simultaneously manage other patients, but it has yet to demonstrate significant benefits over conventional treatment. This is potentially linked to inaccurate robotic representation of personalised physical therapist-patient interaction and lack of practice variability during TST. Hence, we advocate for robotic interventions that preserve the personalised physical therapist-patient interactions when delivering TST for patients across varying practise conditions. We propose a Learning-from-Demonstration framework using Task-Parameterised Gaussian Mixture Models (TPGMM) to learn personalised physical therapist-patient interaction in Task-Specific exercises, mapping patient joint kinematics to therapist-applied torques using few demonstrations. The model is generalised to reconstruct therapist torques in new task variations. The framework was evaluated on physical interactions from 14 mock "therapist-patient" pairs over three tasks of increasing complexity, each with six variations. A benchmark comparison against a Look-Up Table was conducted. The results show both methods reproducing interactions in unseen task variations that deviate slightly from the actual interaction, with TPGMM slightly outperforming LUT. Both methods reproduced interactions that gets increasingly closer to the actual interaction as task complexity increases.

I. INTRODUCTION

Task-Specific Training benefits motor recovery and therapy dosage, but current rehabilitation robots inadequately model personalised therapist-patient forces and practice variability. This work proposes learning therapist-applied interactions from few demonstrations and generalising them across unseen task variations.

  • Motivation: Task-Specific Training and sufficient therapy dosage are positively associated with upper-extremity motor recovery, while robots can increase dosage through controlled, repetitive treatment.Robotic delivery may also free therapists to manage multiple patients simultaneously.
  • Motivation: Robots struggle to adapt their therapist role across dynamic task environments containing varied positions, speeds, and objects.These challenges concern understanding both the task context and the patient interaction.
  • Motivation: Current interaction models inadequately represent therapists’ desired movements, forces, and communication of intent, potentially explaining why robotic TST has not substantially outperformed conventional TST.This limitation persists despite robots’ ability to deliver larger training doses.
  • Research gap: Practice variability is important for skill transfer, but current clinical TST and RHHI approaches rarely incorporate varied task conditions.Capturing personalised physical interaction alone does not teach robots how to apply it across varying conditions.
  • Contribution: The proposed Learning-from-Demonstration framework learns therapist-patient interactions from patient joint kinematics and therapist-applied joint torques, then generalises them to unseen task variations.The interaction model is intended to be therapist-, patient-, and task-specific and to support structured repetition across varying conditions.

II. FRAMEWORK FOR LEARNING PHYSICAL PATIENT–THERAPIST INTERACTION

The framework models physical therapist–patient interaction from patient joint kinematics and therapist-applied torques, then learns a task-specific mapping that generalizes across task conditions. It uses TPGMM-based learning and compares it with a conventional look-up table method.

  • Interaction learning: A Task-Parameterized Gaussian Mixture Model framework captures and generalizes therapist interactions across varying task conditions, alongside a conventional look-up table method.The section presents TPGMM-based learning and introduces LUT as a comparison method.
  • Interaction representation: The framework formulates therapist–patient interaction using patient joint positions, velocities, and therapist-applied joint torques.These quantities define the interaction vector for a D-DOF musculoskeletal model.
  • Interaction representation: Each therapist–patient pair performs tasks across multiple variations and repetitions, with every trial indexed by pair, task, variation, and repetition.A trial has duration T_n and is sampled at a fixed period Δt into interaction vectors.
  • Demonstration organization: The framework stacks sampled interaction profiles across trials to represent patient kinematics and therapist-applied torque profiles for each task.For each pair and task, demonstrations cover all task variations and repetitions.
  • Interaction learning: Learning-from-Demonstration approximates a pair- and task-specific model that maps patient joint kinematics to therapist-applied joint torques.The learned approximation is denoted ˆg_a,e for the unknown interaction model g_a,e.

A. Task-Parameterised Gaussian Mixture Models · 1) Frame Transformation:

The framework uses TPGMM to generalize demonstrated therapist-patient interactions across task conditions while preserving key interaction characteristics. Demonstrations are transformed into task-point reference frames in the patient’s D-DOF joint space, with torque profiles kept consistent across equivalent kinematic configurations.

  • A. Task-Parameterised Gaussian Mixture Models: TPGMM approximates the interaction model and generalizes demonstrations across varying task conditions while preserving demonstrated interaction characteristics.It was selected because prior work found it preserved intended movement features more effectively than DMPs when reproducing unseen task variations.
  • 1) Frame Transformation:: Each demonstration comprises movements between a fixed number P of task points, such as start, via, and end points.A reference frame is assigned to every task point in each interaction profile Γn.
  • 1) Frame Transformation:: For each task point p, the reference frame is defined relative to a known inertial frame using a rotation matrix A(p) and displacement vector b(p).The interaction profile Γn is transformed into each reference frame following Calinon’s formulation.
  • 1) Frame Transformation:: Each interaction vector γn,j is transformed into the pth reference frame, producing a transformed interaction profile Γ(p)n for trial n.Applying the transformation to every interaction vector in a trial yields the frame-specific profile.
  • 1) Frame Transformation:: The transformed profiles from all N trials are stacked to form the demonstration set in the pth reference frame.This assembles the frame-specific data used by the task-parameterized model.
  • 1) Frame Transformation:: Unlike conventional three-dimensional Euclidean TPGMM, this implementation applies TPGMM in the patient’s D-DOF joint space.The reference-frame parameters are therefore defined in the patient’s joint-space representation.
  • 1) Frame Transformation:: Reference frames are identified from the patient’s joint positions and velocities at samples corresponding to reaching each task point.The variables qn,jp and ˙qn,jp denote the joint positions and velocities at sample jp of trial n.
  • 1) Frame Transformation:: No rotational or scaling transformation is tested, and joint torques are not translated between reference frames, ensuring identical kinematics share the same torque profile.The implementation sets A(p)n = ID×D and represents the torque translation component by 0D in b(p)n.

2) Modelling: · 3) Regression:

The framework models demonstrations with a task-parameterised Gaussian mixture and predicts therapist-applied torques for new task variations through reference-frame conditioning and Gaussian Mixture Regression.

  • 2) Modelling:: TPGMM represents demonstrations as a mixture of K Gaussian kernels, each defined by a mixture weight, mean vector, and covariance matrix.The kernels are denoted by {π_k, N(µ_k, Σ_k)} for k=1,…,K.
  • 2) Modelling:: Each Gaussian distribution is parameterised across P reference frames using corresponding sub-Gaussian distributions.The reference-frame parameterisation accounts for task variations.
  • 2) Modelling:: The optimal number of Gaussian kernels K is selected with the Bayesian Information Criterion.This selection determines the model complexity before fitting the frame-specific mixture models.
  • 2) Modelling:: For each reference frame p, a GMM is learned from the transformed demonstrations Γ^(p) using Expectation–Maximisation to maximise observed-data likelihood.The mixture parameters are estimated for all p ∈ [1, 2, …, P].
  • 3) Regression:: For a new task variation, new reference frames are defined from the required joint kinematics at the new task points.These frames are denoted b^(p)_new.
  • 3) Regression:: The learned GMM in each reference frame is conditioned on the new reference frames to obtain frame-specific conditioned Gaussian distributions.The conditioning uses a simplified form because the joint-space transformation matrix is the identity, A^(p)_new = I.
  • 3) Regression:: Conditioned Gaussian distributions from all P reference frames are combined by the product of Gaussians to form the reduced GMM.Gaussian Mixture Regression is then applied to the reduced GMM Θ to estimate therapist-applied joint torques from new patient joint kinematics.

B. Look-Up Table · III. EXPERIMENTAL METHODS

The LUT benchmark retrieves therapist-applied torques from the most similar demonstrated patient kinematics, while the experimental methodology evaluates it against TPGMM through training, validation, generalisation, outcome measures, and statistical analyses.

  • B. Look-Up Table: The LUT benchmark directly stores demonstrated therapist–patient interactions and retrieves the interaction with the most similar joint kinematics.Unlike TPGMM, LUT does not learn a statistical model to generalise interactions across varying task conditions.
  • B. Look-Up Table: A LUT is constructed from patient joint positions, joint velocities, and therapist-applied joint torques recorded during demonstrations.The demonstration set is denoted Γ = [q, ˙q, τ].
  • B. Look-Up Table: For new patient joint kinematics, LUT performs a closest-vector search using Euclidean distance across the demonstration set.The input consists of joint position and velocity, (qjtest, ˙qjtest).
  • B. Look-Up Table: LUT estimates therapist-applied torque by selecting the torque associated with the nearest demonstration sample.The estimated torque is denoted ˆτ jtest.
  • B. Look-Up Table: A low-pass filter with a cut-off frequency of 3 Hz reduces rapid estimated-torque variations caused by switching between neighbouring LUT entries.Filtering is applied after nearest-neighbour torque selection.
  • III. EXPERIMENTAL METHODS: The experimental methodology evaluates the proposed therapist–patient interaction learning framework against the benchmark LUT approach.The protocol covers participant recruitment, data acquisition, data processing, training, validation, generalisation, outcome measures, and statistical analyses.

A. Experimental Protocol · 1) Experimental Procedure:

The study used paired participants who alternated mock therapist and patient roles while performing three task-specific exercises across six task variations with four repetitions each. Patient personas and task parameters defined the experimental conditions.

  • 1) Experimental Procedure:: Participant pairs alternated roles, with one person acting as three patient personas and the other interacting as a therapist during each half-session.Roles were exchanged at the end of each half-session.
  • 1) Experimental Procedure:: Each task comprised sub-tasks performed under specific variations, with two variation parameters having two and three levels.Each task variation was repeated for four trials.
  • 1) Experimental Procedure:: Each therapist–patient pair demonstrated three tasks across six variations, with four repetitions per variation.The protocol indexed pairs as a ∈ {1, . . . , A}, tasks as e ∈ {1, 2, 3}, variations as v ∈ {1, 2, . . . , 6}, and repetitions as r ∈ {1, 2, . . . , 4}.
  • 1) Experimental Procedure:: The study included three patient personas with distinct clinical histories, motor-function profiles, and presentations.The personas ranged from dense right hemiparesis and severe weakness to moderate or mild right-sided impairment.
  • 1) Experimental Procedure:: One exercise required transporting food with utensils through four movement sub-tasks, varying spoon orientation and plate distance.The spoon task included moving from home to the spoon, scooping from a rice bowl, pouring onto a plate, and returning home.
  • 1) Experimental Procedure:: A second exercise required pouring water from a jug through four movement sub-tasks, varying jug volume and bowl distance.Jug volume varied between half and full, while bowl distance included close and middle conditions.

2) Participant Recruitment: … 1) Approximating Patient Joint Kinematics and Therapistcontributed Joint Torque :

The study recruited clinically experienced physiotherapy students and collected synchronized patient upper-body kinematics and therapist interaction wrenches using wearable sensing. These data were filtered, bias-corrected, differentiated, converted to joint torques, and segmented into task phases for interaction-profile construction.

  • 2) Participant Recruitment:: Third-year physiotherapy students with neuro-rehabilitation or sports-therapy placement experience were recruited from the University of Melbourne.The study received ethics approval (#31992) and obtained written informed consent.
  • B. Data Collection: A wearable sensor system was designed to measure therapist-applied force interactions on the patient’s upper body.The system used custom rigid cuffs instrumented with force-torque sensors.
  • B. Data Collection: Patient upper-body joint positions were measured with XSENS Awinda and modeled as a four-link, 10-DOF serial manipulator.The measured configuration was qn,j ∈ R^D=10, spanning the pelvis to the wrist.
  • B. Data Collection: Three 6-DOF RFT80-6A01 sensors measured therapist-patient wrenches at the shoulder, upper arm, and forearm.For each sample, the three sensor wrenches were represented as wi,n,j ∈ R^6.
  • B. Data Collection: Joint positions and wrenches were synchronized in Python and resampled at 100Hz, with ∆t = 0.01s for each trial.Each trial provided joint-position and three-sensor wrench profiles.
  • C. Data Processing: The joint-position and wrench profiles were filtered using fourth-order low-pass filters with a 10Hz cutoff.Wrench measurements were additionally corrected for soft-tissue deformation and cuff-gravity biases before interaction modeling.
  • 1) Approximating Patient Joint Kinematics and Therapistcontributed Joint Torque :: Each interaction profile was defined as Γn = [qn, ˙qn, τn], with velocity estimated by forward differences and filtered at 1.5Hz.Joint torques were obtained by mapping each force-sensor wrench through its Jacobian and summing contributions across interaction points.
  • 1) Approximating Patient Joint Kinematics and Therapistcontributed Joint Torque :: Interaction profiles were segmented by sub-task phases using video-referenced movement-onset timestamps, while task-point kinematics supplied reference frames.Segmentation followed the sub-movement onset at specified task points.

2) Segmentation and Alignment: · D. Generalisation (Variation Split) and Validation (Monte Carlo Sampling) · E. Outcome Measures

Trials were temporally aligned within each task variation using Dynamic Time Warping and normalized to a common time scale. Generalization was evaluated by training on four variations, testing on two unseen variations, and measuring reconstructed torques against therapist-behavior variability.

  • 2) Segmentation and Alignment:: Dynamic Time Warping aligned joint kinematics across trials within each therapist-patient-task-variation to the same number of samples Jζ.The alignment accounted for variability in interaction speed and duration across repetitions.
  • 2) Segmentation and Alignment:: All six aligned task variations were normalized to a common [0, 1] time scale.
  • D. Generalisation (Variation Split) and Validation (Monte Carlo Sampling): Two of six variations were designated unseen, while the therapist-patient-task-specific interaction model ga,e was trained on the remaining four.Only unseen-variation pairs differing by at least one level in both parameters were retained, yielding six valid train-validation-generalisation combinations.
  • D. Generalisation (Variation Split) and Validation (Monte Carlo Sampling): Four Monte Carlo samplings held out one trial from each training variation, ensuring every training trial appeared once in validation.
  • D. Generalisation (Variation Split) and Validation (Monte Carlo Sampling): A separate ga,e model was trained for all combinations and evaluated on both held-out trials and unseen variations.This provided complete coverage of train-validation-generalisation combinations.
  • E. Outcome Measures: Reconstructed torque profiles were considered consistent with intended therapist interaction when they lay within the therapist’s behavior boundaries τζ.Therapist variability was characterized using central behavior and behavior boundaries, such as a 95% confidence interval.
  • E. Outcome Measures: Values below 1 for ϵn and ∆τn,peak indicate reconstructed torques remain within therapist-behavior boundaries, while Cn measures the percentage of normalized time within them.The central behavior was represented non-parametrically by mid-range samples and peak torque because each variation had limited repetitions.

F. Statistical Analysis · IV. RESULTS · A. Participants and Exclusion

The study evaluated TPGMM and LUT reconstruction performance on seen and unseen task variations using defined outcome measures and statistical analyses. Data were aggregated across degrees of freedom and participant conditions, analyzed with repeated-measures ANOVAs, and restricted to the retained participant data after exclusions.

  • F. Statistical Analysis: Outcome measures were averaged across ten DOFs and all train-validation-generalisation combinations, yielding one sample per method, patient persona, outcome measure, and participant.The aggregation was performed separately for validation with seen variations and generalisation with unseen variations; outliers outside 1.5IQR were removed.
  • F. Statistical Analysis: Each outcome measure was analyzed separately for validation and generalisation with a two-way repeated-measures ANOVA testing patient personas, reconstruction methods, and their interaction.This produced six separate ANOVAs after normality testing.
  • IV. RESULTS: TPGMM reconstruction performance was evaluated against LUT for seen and unseen task variations using defined outcome measures and statistical analyses.The results section presents the experimental evaluation of the proposed therapist–patient interaction learning framework.
  • A. Participants and Exclusion: Twenty-four participants without upper-limb or known neurological injury were recruited as 12 pairs, with mean age 25.2 ± 0.5 years and height 169.4 ± 1.8 cm.The sample included 20 female participants, and all used their right hand to enact the three patient personas.
  • A. Participants and Exclusion: The first five pairs were excluded because sensors were mostly disengaged during free interaction, producing minimal recorded interactions.Later participants were instructed to restrict interaction to the 3D-printed cuffs so force-sensor interactions were fully captured.
  • A. Participants and Exclusion: After excluding the first five pairs, data from 14 participants remained for the full analysis.This exclusion resulted from insufficiently captured interactions during the initial sessions.
  • A. Participants and Exclusion: Data from participant #20 in the second variation of the third patient persona were excluded after a communication error corrupted two of four trials.The affected condition was Γζ={20,3,2}, and outcome measures from its training or test samples were removed.

B. Visualisation for τ ζ and ˆτ n … 3) Effects of Patient Persona:

The paper visualizes therapist-torque variability and reconstructions, then evaluates outcome distributions across validation and generalisation cases, methods, and patient personas. Both methods reproduced intended interactions with modest deviations, while persona complexity produced opposite performance trends across cases.

  • B. Visualisation for τ ζ and ˆτ n: Therapist-applied torque varied across four repetitions for a given task variation, with TPGMM and LUT reconstructing the corresponding interaction.The example used τζ={18,2,1} and reconstructed torques τ̂n={18,2,1,3}.
  • C. Distribution of Outcome Measures: Outcome distributions were approximately normal overall, although ε and Δτpeak showed deviations linked to one atypical participant in Personas 2 and 3 for TPGMM.The paper retained this participant to preserve potentially representative population variability.
  • C. Distribution of Outcome Measures: Patient persona significantly affected every outcome measure except Δτpeak in the generalisation case, while method significantly affected every measure except C in validation.The Persona × Method interaction was generally nonsignificant, with an exception reported for Δτpeak.
  • 1) Validation Performance:: Both methods reconstructed therapist-intended interactions effectively in validation, with ε below or around 1 and C around 68%.TPGMM showed poorer fidelity than vector search for finer interaction details, with Δτpeak around 1.2.
  • 3) Effects of Patient Persona:: Persona comparisons showed significant differences between Persona 1 and Personas 2 and 3, but not between Personas 2 and 3.This pattern matched the task design, with Persona 1 simpler and Personas 2 and 3 nearly equivalent in complexity.
  • 3) Effects of Patient Persona:: Increasing task complexity degraded validation performance but improved generalisation performance, with ε increasing and C decreasing in validation and the reverse in generalisation.The changes from Persona 1 to Personas 2 and 3 were statistically significant.

V. DISCUSSION … C. Limitations and Future works

The study extends learning of therapist-patient interaction to complex, varying task-specific exercises, finding that both methods generalize with small differences in performance. Limitations include constrained contact modeling, offline evaluation, and non-clinical participants, motivating integration with rehabilitation robots and post-stroke pilot studies.

  • V. DISCUSSION: The study extends prior interaction-learning work from simple two-point movement to more complex, varying upper-limb task-specific exercises, benchmarking TPGMM against vector search.Both methods learn the relation between patient movement and therapist actions from subsets of task variations.
  • V. DISCUSSION: For seen variations, both methods reconstructed interactions within therapist-behaviour variability, while vector search held a slight advantage over TPGMM.For unseen variations under minimal demonstrations, both deviated slightly from therapist-behaviour variability, with TPGMM showing a small but significant advantage.
  • A. Reduction in Interaction Coverage and Training Samples: Vector search replicated complex interactions across conditions when reconstructing variations within the training dataset, while differences from TPGMM were significantly small in unseen cases.This validates vector search for the evaluated in-dataset variations but indicates limited separation between methods for unseen variations.
  • A. Reduction in Interaction Coverage and Training Samples: The selected variations covered 66% of the interaction workspace, and training used 12 samples out of 24 demonstrations because samples covered 75% of seen variations.The authors suspect consistent therapist behaviour across task variations contributed to vector-search performance and propose studying reduced coverage and training samples.
  • B. Correlation Between Task Complexity and LfD Performance: Both candidate methods improved when generalizing to unseen variations as task complexity increased, indicating a significant relation between task complexity and Learning-from-Demonstration performance.The authors note a possible trade-off between task complexity and therapist-behaviour reproduction in seen and new variations.
  • C. Limitations and Future works: Interaction was constrained to three contact points—clavicle, upper arm, and forearm—which significantly alters participants’ interactions compared with conventional therapy sessions.The constraint simplified system design because no system captured full-body interaction between two humans.
  • C. Limitations and Future works: Physiotherapy students’ lack of clinical experience may have produced differing interpretations of patient personas and greater interaction variability than in actual practice.Students were recruited for availability and to avoid clinical habits that could bias engagement with the system.
  • C. Limitations and Future works: Offline evaluation used robot-unconstrained patient kinematics, real-time human-in-the-loop efficacy remains unvalidated, and TPGMM training lasted 2 - 4 minutes on a standard CPU.The authors therefore avoid claiming direct applicability to neuro-rehabilitation, recommending robotic integration and post-stroke pilot studies.
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