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Prognostic Framework for Robotic Manipulators Operating Under Dynamic Task Severities

Ayush Mohanty, Jason Dekarske, Stephen K. Robinson, Sanjay Joshi, Nagi Gebraeel

TL;DR

This work addresses predicting the Remaining Useful Life (RUL) of robotic manipulators operating under dynamically varying task severities. It introduces a prognostic framework that couples a Continuous-Time Markov Chain (CTMC) task-severity model with a Brownian motion degradation signal whose drift depends on severity, and uses periodic calibrations to keep data homogeneous. Two RLD estimation approaches are proposed: a closed-form inverse-Gaussian-based method using the stationary distribution of task severity, and a Monte Carlo simulation method, with theoretical results showing their equivalence under mild conditions. Experiments on planar and spatial robot fleets with physics-based simulators demonstrate that higher proportions of severe tasks shorten RUL, and the closed-form approach achieves substantial computational gains while maintaining accuracy. The framework supports Bayesian updating of model parameters and enables what-if analyses of future task mixes, offering practical, scalable prognostics for robot fleets.

Abstract

Robotic manipulators are critical in many applications but are known to degrade over time. This degradation is influenced by the nature of the tasks performed by the robot. Tasks with higher severity, such as handling heavy payloads, can accelerate the degradation process. One way this degradation is reflected is in the position accuracy of the robot's end-effector. In this paper, we present a prognostic modeling framework that predicts a robotic manipulator's Remaining Useful Life (RUL) while accounting for the effects of task severity. Our framework represents the robot's position accuracy as a Brownian motion process with a random drift parameter that is influenced by task severity. The dynamic nature of task severity is modeled using a continuous-time Markov chain (CTMC). To evaluate RUL, we discuss two approaches -- (1) a novel closed-form expression for Remaining Lifetime Distribution (RLD), and (2) Monte Carlo simulations, commonly used in prognostics literature. Theoretical results establish the equivalence between these RUL computation approaches. We validate our framework through experiments using two distinct physics-based simulators for planar and spatial robot fleets. Our findings show that robots in both fleets experience shorter RUL when handling a higher proportion of high-severity tasks.

Prognostic Framework for Robotic Manipulators Operating Under Dynamic Task Severities

TL;DR

This work addresses predicting the Remaining Useful Life (RUL) of robotic manipulators operating under dynamically varying task severities. It introduces a prognostic framework that couples a Continuous-Time Markov Chain (CTMC) task-severity model with a Brownian motion degradation signal whose drift depends on severity, and uses periodic calibrations to keep data homogeneous. Two RLD estimation approaches are proposed: a closed-form inverse-Gaussian-based method using the stationary distribution of task severity, and a Monte Carlo simulation method, with theoretical results showing their equivalence under mild conditions. Experiments on planar and spatial robot fleets with physics-based simulators demonstrate that higher proportions of severe tasks shorten RUL, and the closed-form approach achieves substantial computational gains while maintaining accuracy. The framework supports Bayesian updating of model parameters and enables what-if analyses of future task mixes, offering practical, scalable prognostics for robot fleets.

Abstract

Robotic manipulators are critical in many applications but are known to degrade over time. This degradation is influenced by the nature of the tasks performed by the robot. Tasks with higher severity, such as handling heavy payloads, can accelerate the degradation process. One way this degradation is reflected is in the position accuracy of the robot's end-effector. In this paper, we present a prognostic modeling framework that predicts a robotic manipulator's Remaining Useful Life (RUL) while accounting for the effects of task severity. Our framework represents the robot's position accuracy as a Brownian motion process with a random drift parameter that is influenced by task severity. The dynamic nature of task severity is modeled using a continuous-time Markov chain (CTMC). To evaluate RUL, we discuss two approaches -- (1) a novel closed-form expression for Remaining Lifetime Distribution (RLD), and (2) Monte Carlo simulations, commonly used in prognostics literature. Theoretical results establish the equivalence between these RUL computation approaches. We validate our framework through experiments using two distinct physics-based simulators for planar and spatial robot fleets. Our findings show that robots in both fleets experience shorter RUL when handling a higher proportion of high-severity tasks.

Paper Structure

This paper contains 33 sections, 3 theorems, 35 equations, 7 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Robot's Faults Diagnostics and Prognostics
  4. Prognostics Under Dynamic Operating Conditions
  5. Degradation Modeling Framework of Robot
  6. Key Modeling Assumptions
  7. Task Severity Model
  8. Robot Position Accuracy Model
  9. Bayesian Updating of Model Parameters
  10. Update of Severity Model Parameters
  11. Update of Accuracy Model Parameters
  12. Remaining Lifetime Distribution of Robot
  13. Approach 1: Effective Degradation Rate
  14. Approach 2: Monte-Carlo Simulation
  15. Implementation Procedure
  16. ...and 18 more sections

Key Result

Proposition 1

At any inspection epoch $c_k$, the posterior distribution of $\alpha$ and $\beta$ follows a bivariate normal with mean ($\mu_{\alpha}, \mu_{\beta}$), variance ($\sigma_{\alpha}^2, \sigma_{\beta}^2$) and correlation coefficient $\rho$ with the following values:

Figures (7)

  • Figure 1: The proposed prognostic framework for robotic manipulators
  • Figure 2: In the proposed framework, an accuracy test task is performed periodically to inspect the position accuracy and estimate RUL
  • Figure 3: This is a schematic of the planar representation of the UR5e robot with rigid bodies labeled. The kinematic and inertial properties of the robot are accurate with the unstudied joints locked. The payload is rigidly attached to the end of the forearm link (not pictured).
  • Figure 4: This 3D rendering of the Panda robotic arm depicts the final configuration of the arm for the commanded end-effector position with the payload. The payload was initially grasped from the table's surface. The payload is pitched because it slid while in transit.
  • Figure 5: Position accuracy of five (a) planar, and (b) spatial robots
  • ...and 2 more figures

Theorems & Definitions (13)

  • Remark 1
  • Definition 1
  • Proposition 1
  • proof
  • Remark 2
  • Proposition 2: adapted from serfozo2009
  • proof
  • Definition 2
  • Definition 3
  • Lemma 1
  • ...and 3 more