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RoKON: Efficient and Adaptive Data-Enabled Predictive Control for Robotic Manipulation

Akshun Sharma, Zhongqi Wei, Buqing Ou, Frederike Dümbgen

arXiv:2610.35458v1cs.RO

TL;DR

Accurate models are difficult to obtain for robotic interactions involving contact and friction, and collecting physical robot data can be costly. RoKON combines a nonlinear Gaussian-kernel predictor, a damped Gauss–Newton solver, and a hybrid data buffer. In simulated pushing across changing-friction surfaces, the paper reports that control inputs can be computed within the available sampling period.

  • Problem

    Contact, friction, and actuator dynamics can make accurate environment models difficult to obtain, while collecting physical robot data requires substantial time, supervision, and hardware access.

    Source: §I · p. 1

  • Method

    RoKON combines a nonlinear Gaussian-kernel predictor and damped Gauss–Newton updates with a fixed-capacity hybrid buffer that incorporates informative online data while retaining protected offline data.

    Source: §I · pp. 1–2, B. Hybrid Buffer · p. 5

  • Results

    On robotic pushing across surfaces with unknown, changing friction, the proposed method computes control inputs within the available sampling period.

    Source: §V · pp. 7–8

  • Takeaways & Limitations

    The hybrid buffer’s protected offline data and informative online updates let the predictor account for changing interaction dynamics while maintaining bounded memory and computation.

    Source: B. Hybrid Buffer · p. 5, §V · p. 8

Abstract

from arXiv · show

Data-enabled predictive control has recently emerged as a promising control paradigm, enabling a transparent optimal-control formulation without the need to learn an explicit dynamics model. This paper presents a number of extensions paving the path towards its use in real-time robotics tasks. Following recent work, we utilize a nonlinear predictor based on Gaussian kernels to represent the relationship between input and output data. We propose a damped Gauss-Newton method that enables real-time control by efficiently exploiting the least-squares structure of the control problem. In addition, we introduce a hybrid buffer management strategy that incorporates informative online data while retaining relevant offline data, allowing the predictor to account for changes in the dynamics. We demonstrate the tracking performance and computational suitability of the proposed method in MuJoCo using a Franka Research 3 arm pushing a block across surface, without prior knowledge of its changing friction values.

I. INTRODUCTION

Robotic contact and friction make accurate environment models difficult, while DeePC offers control directly from measured input–output data. This section motivates RoKON’s adaptive nonlinear predictor and efficient solver, then outlines DeePC’s trajectory-based formulation.

I. INTRODUCTION

  • Contact, friction, and actuator dynamics can make accurate models costly to obtain, while physical data collection requires time, supervision, and hardware access.Exploratory actions may also cause task failures or hardware damage.Source: §I · p. 1
  • Standard DeePC’s trajectory parameterization is exact only for controllable LTI systems, so nonlinear robotic applications commonly use local linear representations or lifted features..Source: §I · p. 1
  • RoKDeePC represents nonlinear multistep input–output behavior with kernels, but its nonconvex optimization and fixed offline dataset raise computation and adaptation challenges.RoKON retains nonlinear Gaussian-kernel dependence on future inputs and updates a fixed-capacity hybrid buffer with informative online measurements.Source: §I · p. 1
  • Damped Gauss–Newton updates exploit the control problem’s least-squares structure to solve the nonconvex problem efficiently..Source: §I · p. 1
  • RoKON is validated in MuJoCo robotic pushing under varying friction, with favorable performance reported against MPC and state-of-the-art data-enabled predictive control baselines..Source: §I · p. 2

A. Data Driven Control and DeePC

  • DeePC constructs control actions directly from measured input–output data, embedding a data-based trajectory representation in a receding-horizon optimization without identifying a state-space model.For a controllable LTI system with sufficiently persistently exciting input, Hankel-matrix columns parameterize admissible trajectories.Source: §I · p. 1, A. Data Driven Control and DeePC · p. 2
  • DeePC maps recorded trajectories to candidate future input–output trajectories through coefficients, then applies only the first optimized input before updating measurements and resolving.The input data must be sufficiently persistently exciting to represent admissible trajectories.Source: A. Data Driven Control and DeePC · p. 2

B. Robust and Kernelized DeePC (RoKDeePC)

RoKDeePC extends data-enabled predictive control to nonlinear systems by using a regularized kernel predictor for future outputs. Its Gaussian-kernel dependence on future inputs makes the control problem nonconvex, motivating computationally efficient solution methods.

B. Robust and Kernelized DeePC (RoKDeePC)

  • RoKDeePC replaces DeePC’s linear predictor with a regularized kernel-based multistep predictor for nonlinear systems.The predictor represents each future-output component as a function of past inputs, past outputs, and future inputs.Source: B. Robust and Kernelized DeePC… · p. 3
  • Regularized kernel regression constructs each multistep predictor from recorded past-input, past-output, and future-input trajectories.The Gaussian kernel provides a smooth similarity measure for nonlinear relationships between trajectories.Source: B. Robust and Kernelized DeePC… · p. 3
  • The Gaussian kernel’s nonlinear dependence on future inputs makes the control problem nonconvex, although it is convex in trajectory coefficients for fixed inputs under stated conditions.Those conditions include Q ⪰ 0, λg, λk ≥ 0, and a convex output-constraint set.Source: B. Robust and Kernelized DeePC… · p. 3
  • With output constraints inactive, a closed-form coefficient solution reduces optimization to choosing future inputs; RoKON retains the nonlinear kernel and replaces projected-gradient descent with damped Gauss–Newton steps.A globally linear future-input kernel assumption instead yields a quadratic program, but may not fit configuration-dependent robotic dynamics or nonlinear actuation.Source: B. Robust and Kernelized DeePC… · p. 3

III. METHOD

The method has two components: a kernelized data-enabled predictor with Gauss–Newton updates, and a hybrid buffer for adapting to observed dynamics changes.

III. METHOD

  • The method combines a kernelized data-enabled predictor with Gauss–Newton update steps for fast, real-time control..Source: §III · p. 3
  • A hybrid buffer adapts the predictor when observed dynamics change..Source: §III · p. 3
  • The method’s two components address computation and adaptation, respectively..Source: §III · p. 3

A. Kernelized Data Predictor with Gauss–Newton updates

The method retains the nonlinear Gaussian-kernel RoKDeePC objective and uses damped Gauss–Newton updates to exploit its nonlinear least-squares structure. Local approximations, damping, and input projection support efficient constrained updates.

A. Kernelized Data Predictor with Gauss–Newton updates

  • Damped Gauss–Newton exploits the nonlinear least-squares structure while retaining the Gaussian kernel’s nonlinear dependence on future inputs.Unlike the prior restriction to a kernel globally linear in the future input sequence, this method retains the nonlinear kernel.Source: A. Kernelized Data Predictor with… · p. 3
  • The Gaussian kernel vector is locally linearized using its analytical Jacobian, then reevaluated exactly after each control-sequence update.The residual Jacobian and residual vector are evaluated at the current iteration to form the local approximation.Source: A. Kernelized Data Predictor with… · p. 4
  • The damped Gauss–Newton direction is obtained from a local least-squares problem, with the damping coefficient governing the update.The passage identifies the direction as a local least-squares solution and defines η as the damping coefficient.Source: A. Kernelized Data Predictor with… · p. 4
  • Candidate inputs are projected into the feasible set, and cost-increasing steps are rejected and recomputed with greater damping.The cost check uses the original nonlinear objective.Source: A. Kernelized Data Predictor with… · p. 4
  • The previous optimized sequence is shifted to initialize the next receding-horizon optimization; only its first input is applied.The terminal value is repeated to preserve the horizon length.Source: A. Kernelized Data Predictor with… · p. 4

B. Hybrid Buffer

The hybrid buffer combines fixed offline trajectories with replaceable offline and online data. It admits online trajectories based on one-step prediction residuals and rebuilds predictor matrices when the buffer changes.

B. Hybrid Buffer

  • A buffer entry is built from a contiguous offline input–output trajectory window, avoiding artificial transitions within each column.Each window contains past and future input and output components.Source: B. Hybrid Buffer · p. 5
  • The buffer preserves a fixed set of offline trajectory columns while allowing replaceable columns to incorporate new measurements.Protected offline columns remain unchanged, preventing complete forgetting during online adaptation.Source: B. Hybrid Buffer · p. 5
  • Online admission depends on the one-step-ahead prediction residual, which measures mismatch between predicted and observed output independently of the reference.An admitted column is appended before the buffer is full; afterward, it replaces the oldest replaceable entry, never a protected column.Source: B. Hybrid Buffer · p. 5
  • Changing buffer contents requires reconstruction of the trajectory, kernel, and solver matrices used by the predictor.The complete algorithm reconstructs these matrices from an immutable copy of the current buffer.Source: B. Hybrid Buffer · p. 5

IV. EXPERIMENTAL EVALUATION

The section covers the experimental setup and implementation, the experiments conducted, and discussion of their results.

IV. EXPERIMENTAL EVALUATION

  • The section presents experimental setup and implementation details.Source: §IV · p. 5
  • The section describes the experiments conducted.Source: §IV · p. 5
  • The section discusses the experimental results.Source: §IV · p. 5

A. Setup

The evaluation setup uses a Franka Research 3 arm to push a block across surfaces with varying friction. The controller tracks a constant velocity without an explicit dynamics or friction model, using measured force–velocity data.

A. Setup

  • The MuJoCo task uses a Franka Research 3 arm to push a 0.5 kg block across surfaces with friction coefficients 0.2, 0.5, and 0.25.The block measures 0.10 × 0.10 × 0.05 m.Source: A. Setup · p. 5
  • The control objective is constant-velocity tracking across changing friction using measured force–velocity data, without an explicit dynamics or friction model.The force is the input and block velocity along the pushing axis is the output.Source: A. Setup · p. 5
  • The controller starts from a compact dataset collected on the starting surface, without knowing friction or transition location, and must adapt online in real time.Source: A. Setup · p. 5
  • Experiments use a 0.03 s sampling period, past horizon 2, prediction horizon 5, and a 0–8 N force range.Source: A. Setup · p. 5

1) Uniform-Friction Experiments:

The uniform-friction experiments test constant-velocity tracking when friction stays unchanged during each run. Online adaptation is disabled, and the offline buffer is collected using piecewise-constant force commands.

1) Uniform-Friction Experiments:

2) Varying-Friction Experiment:

The varying-friction experiment tests tracking and online adaptation as the block crosses three surfaces, without advance information about later friction values or transition locations. Four controllers are compared with RoKON.

2) Varying-Friction Experiment:

B. Implementation

The implementation combines configured kernel and control parameters with asynchronous, batched predictor reconstruction, while the low-level controller maps desired pushing force to joint torques. The supplied results describe tracking on uniform and changing-friction surfaces.

B. Implementation

  • Kernel parameters are manually tuned and fixed at σ² = 4 and γ = 0.02, alongside manually set control parameters.Source: B. Implementation · p. 6
  • Admitted Hankel columns are batched for reconstruction by a background CPU worker, while the current predictor remains in use until an atomic model swap.Buffer capacity bounds reconstruction cost, and background execution avoids delaying online optimization.Source: B. Implementation · p. 6

Low-Level Controller:

  • A 1 kHz low-level arm controller maps the desired Cartesian wrench to joint torques while maintaining end-effector pose in non-pushing directions.Source: Low-Level Controller · p. 6

1) Uniform-Friction Experiments:

2) Varying-Friction Experiment:

  • Stribeck MPC and RoKDeePC fail to reach the third surface as friction changes, while RoKON achieves the lowest complete-run RMSE and best tracking on surfaces two and three.Linear DeePC completes the run with moderate tracking error; Table I reports RMSE, Hankel-column counts, and mean computation time.Source: 2) Varying-Friction Experiment · p. 6
  • Using a linear predictor yields a convex quadratic program, avoiding repeated kernel evaluations, Jacobian calculations, and nonlinear solver iterations.Source: 2) Varying-Friction Experiment · p. 7

3) Ablation Study:

The ablation varies online adaptation, protected buffer columns, residual-based admission, and the solver. The conclusion identifies physical-arm testing and broader manipulation conditions as future work.

3) Ablation Study:

  • Without online adaptation, RMSE is approximately 0.0029 m/s on the first surface and 0.0170 m/s on the second; the block does not reach the third.Source: 3) Ablation Study · p. 7
  • Removing protected columns raises third-surface RMSE to approximately 0.0415 m/s; previously observed behaviors may be progressively removed from the buffer.Source: 3) Ablation Study · p. 7
  • Without residual-based admission, velocity collapses on the second surface and the block does not reach the third.This variant admits every valid completed trajectory without requiring a meaningful prediction mismatch.Source: 3) Ablation Study · p. 7
  • Direct nonlinear optimization yields the lowest completed-trajectory RMSE among variants but takes 13.27 ms per update, versus 3.72 ms for damped Gauss–Newton.Source: 3) Ablation Study · p. 7

V. CONCLUSIONS

  • Future work will evaluate the method on a physical FR3 arm and extend testing to multidirectional manipulation, different objects, and more complex contact conditions.Source: §V · p. 8
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