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Reliability of Single-Level Equality-Constrained Inverse Optimal Control

Filip Bečanović, Kosta Jovanović, Vincent Bonnet

TL;DR

This paper tackles the computational bottleneck of inverse optimal control (IOC) in human motion by introducing a single-level reformulation of the traditional bilevel IOC that relies on KKT conditions of the inner optimal-control problem. The method jointly optimizes behavioral parameters $m{ heta}$ and corresponding inner-loop variables, enabling gradient-based solving of a single NLP and yielding equivalent results to bilevel formulations in the presence of noise. Through a simulated 2-DOF planar reaching task with human-like cost functions, the approach demonstrates strong noise robustness and achieves a roughly 15-fold speedup over standard bilevel IOC, while highlighting identifiability considerations. The work suggests that single-level IOC is a promising, scalable option for equality-constrained motion-generation models and lays groundwork for future extensions to inequality-constrained OCPs and real human data.

Abstract

Inverse optimal control (IOC) allows the retrieval of optimal cost function weights, or behavioral parameters, from human motion. The literature on IOC uses methods that are either based on a slow bilevel process or a fast but noise-sensitive minimization of optimality condition violation. Assuming equality-constrained optimal control models of human motion, this article presents a faster but robust approach to solving IOC using a single-level reformulation of the bilevel method and yields equivalent results. Through numerical experiments in simulation, we analyze the robustness to noise of the proposed single-level reformulation to the bilevel IOC formulation with a human-like planar reaching task that is used across recent studies. The approach shows resilience to very large levels of noise and reduces the computation time of the IOC on this task by a factor of 15 when compared to a classical bilevel implementation.

Reliability of Single-Level Equality-Constrained Inverse Optimal Control

TL;DR

This paper tackles the computational bottleneck of inverse optimal control (IOC) in human motion by introducing a single-level reformulation of the traditional bilevel IOC that relies on KKT conditions of the inner optimal-control problem. The method jointly optimizes behavioral parameters and corresponding inner-loop variables, enabling gradient-based solving of a single NLP and yielding equivalent results to bilevel formulations in the presence of noise. Through a simulated 2-DOF planar reaching task with human-like cost functions, the approach demonstrates strong noise robustness and achieves a roughly 15-fold speedup over standard bilevel IOC, while highlighting identifiability considerations. The work suggests that single-level IOC is a promising, scalable option for equality-constrained motion-generation models and lays groundwork for future extensions to inequality-constrained OCPs and real human data.

Abstract

Inverse optimal control (IOC) allows the retrieval of optimal cost function weights, or behavioral parameters, from human motion. The literature on IOC uses methods that are either based on a slow bilevel process or a fast but noise-sensitive minimization of optimality condition violation. Assuming equality-constrained optimal control models of human motion, this article presents a faster but robust approach to solving IOC using a single-level reformulation of the bilevel method and yields equivalent results. Through numerical experiments in simulation, we analyze the robustness to noise of the proposed single-level reformulation to the bilevel IOC formulation with a human-like planar reaching task that is used across recent studies. The approach shows resilience to very large levels of noise and reduces the computation time of the IOC on this task by a factor of 15 when compared to a classical bilevel implementation.

Paper Structure

This paper contains 10 sections, 20 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methods
  3. Optimal Control
  4. Inverse Optimal Control
  5. Bilevel Optimization and Single-Level Reformulation
  6. Optimal Control of Robot Arm Trajectory
  7. Numerical Experiments
  8. Optimal Control of Robot Arm Trajectory
  9. Noisy Inverse Optimal Control
  10. Conclusion

Figures (3)

  • Figure 1: Solutions of the robot-arm OCP \ref{['eq:robot-arm-ocp']} with different objective functions. All important constants defined in Section \ref{['sec:experiments:robot']}.
  • Figure 2: Heatmaps of the errors in parameter and trajectory retrieval when solving the single-level IOC problem \ref{['eq:single-level-ioc']} with noisy data using Algorithm \ref{['alg:single-level']}.
  • Figure 3: Joint trajectories involved in the noisy IOC from Section \ref{['sec:experiments:ioc']} and the heatmaps from Figure \ref{['fig:noise-heatmap']} for two different levels of noise.