Contact-Robust Trajectory Planning Via Parametric Sensitivity Analysis for Hybrid Robotic Systems
Tommaso Belvedere, James Zhu, Marco Cognetti, Paolo Robuffo Giordano
AI summary
Problem
Uncertain system parameters often cause unintended contact loss or slip in hybrid robotic systems, but existing sensitivity tools fail to accurately model the discrete jumps inherent to contact events. This gap prevents the generation of motion plans that are intrinsically robust to real-world parameter variations.
Approach
The authors extend parametric sensitivity analysis to hybrid dynamics by deriving a unified reset rule for state sensitivities across contact events. These sensitivities are used to construct safety tubes that constrain trajectory optimization, ensuring contact forces stay within feasible bounds under uncertainty.
Key results
- Unified first-order sensitivity formulation for hybrid dynamics, guard conditions, and reset maps
- Extended sensitivity analysis to correct switching time approximation errors near impacts
- Sensitivity-based tube construction for robust constraint satisfaction under bounded parametric uncertainty
- Validation on SLIP hopper and planar quadruped models demonstrating suppression of unintended contact transitions
Why it matters
Provides a computationally efficient, model-based foundation for designing safe and reliable dynamic locomotion and manipulation in uncertain real-world environments.
Abstract
In this paper, we combine first-order approxima- tions of hybrid systems (i.e., the so-called saltation matrix) with previous works on parametric sensitivity for continuous systems to propose a general framework for robust trajectory optimization of hybrid systems subject to parametric uncer- tainties. A method for computing parametric sensitivities of both continuous dynamics and hybrid events is presented. The obtained “hybrid parametric sensitivity” is then combined with sensitivity-based tubes that encapsulate all possible perturbed states and control trajectories given a known bounded range for the uncertain parameters. The proposed method is then applied to the problem of planning robust trajectories for legged robot systems, which allows obtaining trajectories that remain feasible w.r.t. the contact constraints even in presence of uncertainties in the dynamics, guard conditions, and reset maps. We also illustrate one of the fundamental limitations of first-order approximations, that is, the fact that the sensitivity reset time is fixed, and propose an extension to the sensitivity analysis that can form the basis for future developments.