Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

System Identification For Constrained Robots

Bohao Zhang, Daniel Haugk, Ram Vasudevan

TL;DR

Constrained robots with closed kinematic chains pose challenges for traditional inertial and friction parameter identification. The authors develop an optimization-based identification framework for fully actuated constrained systems that uses a regressor $Y(q,\dot q,\ddot q)$, base parameters $\pi$, and a transformation $\theta = P_b(\pi - K_d\theta_d) + P_d\theta_d$, together with a fully-actuated representation $\dot q = G(q)\dot q_a$ and LMIs to enforce physical realizability, enhanced by iterative weighted least squares for noise robustness. The method is validated on the Digit humanoid (42 DoF), demonstrating superior tracking with identified parameters compared to manufacturer values in both inverse-dynamics control and forward-simulation contexts, with the implementation released publicly. This work enables more accurate, safe, model-based control for constrained humanoid robots and could broadly improve performance in legged robots with closed-chain constraints.

Abstract

Identifying the parameters of robotic systems, such as motor inertia or joint friction, is critical to satisfactory controller synthesis, model analysis, and observer design. Conventional identification techniques are designed primarily for unconstrained systems, such as robotic manipulators. In contrast, the growing importance of legged robots that feature closed kinematic chains or other constraints, poses challenges to these traditional methods. This paper introduces a system identification approach for constrained systems that relies on iterative least squares to identify motor inertia and joint friction parameters from data. The proposed approach is validated in simulation and in the real-world on Digit, which is a 20 degree-of-freedom humanoid robot built by Agility Robotics. In these experiments, the parameters identified by the proposed method enable a model-based controller to achieve better tracking performance than when it uses the default parameters provided by the manufacturer. The implementation of the approach is available at https://github.com/roahmlab/ConstrainedSysID.

System Identification For Constrained Robots

TL;DR

Constrained robots with closed kinematic chains pose challenges for traditional inertial and friction parameter identification. The authors develop an optimization-based identification framework for fully actuated constrained systems that uses a regressor , base parameters , and a transformation , together with a fully-actuated representation and LMIs to enforce physical realizability, enhanced by iterative weighted least squares for noise robustness. The method is validated on the Digit humanoid (42 DoF), demonstrating superior tracking with identified parameters compared to manufacturer values in both inverse-dynamics control and forward-simulation contexts, with the implementation released publicly. This work enables more accurate, safe, model-based control for constrained humanoid robots and could broadly improve performance in legged robots with closed-chain constraints.

Abstract

Identifying the parameters of robotic systems, such as motor inertia or joint friction, is critical to satisfactory controller synthesis, model analysis, and observer design. Conventional identification techniques are designed primarily for unconstrained systems, such as robotic manipulators. In contrast, the growing importance of legged robots that feature closed kinematic chains or other constraints, poses challenges to these traditional methods. This paper introduces a system identification approach for constrained systems that relies on iterative least squares to identify motor inertia and joint friction parameters from data. The proposed approach is validated in simulation and in the real-world on Digit, which is a 20 degree-of-freedom humanoid robot built by Agility Robotics. In these experiments, the parameters identified by the proposed method enable a model-based controller to achieve better tracking performance than when it uses the default parameters provided by the manufacturer. The implementation of the approach is available at https://github.com/roahmlab/ConstrainedSysID.
Paper Structure (19 sections, 1 theorem, 38 equations, 5 figures, 4 tables)

This paper contains 19 sections, 1 theorem, 38 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions and Organization
  4. Preliminaries
  5. Equations of Motion of Constrained Systems
  6. Regressor Matrix
  7. Fully-Actuated Representation
  8. System Identification For Fully-Actuated Constrained Systems
  9. Experiments
  10. Digit Overview
  11. Implementation Details
  12. Parameters Verification
  13. Inverse Dynamics Validation
  14. Forward Integration Prediction Validation
  15. Inverse Dynamics Controller Experiment
  16. ...and 4 more sections

Key Result

Theorem 2

Suppose at time $t$, the actuated joint position, velocity, and acceleration are $q_a(t)$, $\dot{q}_a(t)$, and $\ddot{q}_a(t)$, respectively. Let $G(q(t))\in \mathbb{R}^{n\times n_a}$ be a matrix whose unactuated rows are defined as and whose actuated rows are defined as where $J_u(q(t)) \in \mathbb{R}^{n_c\times n_u}$ and $J_a(q(t)) \in \mathbb{R}^{n_c\times n_a}$ are the collection of unactu

Figures (5)

  • Figure 1: This paper proposes a system identification method for systems with constraints such as the humanoid, Digit (image on left). Note that Digit has a closed loop kinematic constraint in each of its legs. By using the algorithm developed in this paper, one can identify the inertial and friction parameters of the system from data. To illustrate the utility of this method, this paper compared the performance of a model based tracking controller to track a user-specified trajectory. The tracking performance of the controller was significantly less when using the parameters identified by the algorithm developed in this paper (drawn in red on the right) when compared to using the parameters specified by the manufacturer (drawn in blue on the right). The actual behavior of the robot while following the user-specified trajectory using the parameters identified by the algorithm developed in this paper can be seen on the top right of the image at 4 time instances.
  • Figure 2: This illustrates the closed-loop structure on the legs of Digit. The orange arrows show the rotation axes of all actuated joints (motors). The blue arrows show the rotation axes of all unactuated joints. The purple arrows show the rotation axes of all springs (shin and heel-spring), which are assumed to be fixed in this paper (see Assumption \ref{['ass: sp']}). The green lines show how these joints are connected to be closed-loops.
  • Figure 3: Validation experiment by comparing measured torque and estimated torque on the left leg. The torque residual based on identified parameters is plotted in red. The torque residual based on manufacturer provided parameters is plotted in blue. The data shown is distinct from that used in identification.
  • Figure 4: Validation experiment by comparing the estimated trajectory from ode15s forward integration and the ground truth data set on the left leg. The measured trajectory is plotted in black. The estimated trajectory using identified parameters is plotted in red. The estimated trajectory using manufacturer provided parameters is plotted in blue. Note that we performed the validation by separating the data set into 31 segments, where the initial condition of the ode15s simulation starts from the beginning of each segment. The estimated trajectory between two adjacent segments is connected with vertical dotted lines.
  • Figure 5: The plots show the tracking error of applying an inverse dynamics controller to track a desired trajectory of a sine wave with a maximum velocity of $5$ rad/s for all actuated joints on the left leg. We evaluate how the controller performs when integrated with identified parameters versus the manufacturer provided parameters. The tracking error corresponding to identified parameters is plotted in red. The tracking error corresponding to manufacturer provided parameters is plotted in blue. The desired trajectories shown are distinct from that used in identification.

Theorems & Definitions (2)

  • Theorem 2
  • Remark 4