Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1507.07067

Compensation of Nonlinear Torsion in Flexible Joint Robots: Comparison of Two Approaches

Michael Ruderman
View original source ↗Read source document ↗Export metadata ↓

Abstract

Flexible joint robots, in particularly those which are equipped with harmonic-drive gears, can feature elasticities with hysteresis. Under heavy loads and large joint torques the hysteresis lost motion can lead to significant errors of tracking and positioning of the robotic links. In this paper, two approaches for compensating the nonlinear joint torsion with hysteresis are described and compared with each other. Both methods assume the measured signals available only on the motor side of joint transmissions. The first approach assumes a rigid-link manipulator model and transforms the desired link trajectory into that of the motor drives by using the inverse dynamics and inverse hysteresis map. The second approach relies on the modeling of motor drives and inverse hysteresis and uses the generalized momenta when predicting the joint torsion. Both methods are discussed in details along with a numerical example of two-link planar manipulator under gravity.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Michael Ruderman. 2015-08-22. Compensation of Nonlinear Torsion in Flexible Joint Robots: Comparison of Two Approaches. https://doi.org/10.1109/tie.2016.2574299

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Predicted-Flow Control Barrier Functions for Real-Time Safe Optimal Control

Control barrier functions (CBFs) provide real-time safety guarantees through pointwise conditions on the state. However, synthesizing a valid CBF is difficult and the resulting controllers are myopic. To address myopia, this article introduces predicted-flow control barrier functions (P-CBFs), which generalize the CBF from a function of the current state to a functional of a predicted flow under a parametrized control plan over a finite prediction horizon. For safety, a P-CBF can certify that the predicted flow is in a safe set over the entire prediction horizon. However, candidate P-CBFs suffer from the same challenge as candidate CBFs, namely, control constraints make it difficult to guarantee that the P-CBF is valid. This article resolves this challenge by introducing a terminal candidate P-CBF requiring that the predicted flow end in a backup safe set at the terminal time, and a planning-time shift that modulates the prediction horizon, providing an additional degree of freedom to ensure feasibility. The real-time control and the evolution of the control-plan parameter and planning-time shift are determined jointly by a single convex optimization that is guaranteed to be feasible and renders the associated safe set forward invariant. The resulting safe optimal flow control provides a safety certificate over the entire prediction horizon and unifies finite-horizon integral-cost optimization with safety certification. This optimization reduces to a quadratic program (QP) if the control constraints are a convex polytope. The QP implementation, termed FlowBarrier, is validated on a nonholonomic ground robot navigating a dense environment. FlowBarrier is compared to nonlinear model predictive control and two CBF-based safety filter methods across 100 trials, where FlowBarrier achieves the highest goal-reaching rate, zero safety violations, and the lowest computation time.

eess.SY↗
arXiv2026

Sufficient and Necessary Continuous Barrier-like Conditions for Discrete-Time Stochastic Reach-Avoid Verification

This paper develops necessary and sufficient barrier-like characterizations using continuous barrier functions for infinite-horizon reach-avoid verification of discrete-time stochastic systems. Existing results establish necessary and sufficient conditions in terms of functional inequalities involving measurable or lower semicontinuous barrier functions. However, the limited regularity of such functions may hinder their numerical approximation and computational synthesis. Building on our previous barrier-like condition for finite-horizon reach-avoid verification, we show that this condition can also be used for infinite-horizon reach-avoid verification and, under a uniform absolute continuity condition on the transition kernels, admits a continuous barrier function whenever the exact reach-avoid probability is strictly larger than the prescribed threshold for every state in the initial set. We further show that the resulting continuous barrier function can be uniformly approximated by a polynomial one while preserving the required barrier-like conditions. For polynomial systems, we formulate these conditions as polynomial positivity constraints over compact basic semialgebraic sets. Putinar's Positivstellensatz then converts the positivity conditions into sum-of-squares (SOS) certificates, yielding semidefinite programming (SDP) formulations for synthesizing polynomial barrier functions. We establish both soundness and completeness of the resulting SOS-based procedure. Finally, two numerical examples illustrate the theoretical results and demonstrate the resulting SDP approach.

eess.SY↗
arXiv2026

Sufficient and Necessary Smooth Barrier-like Conditions for Continuous-Time Stochastic Reach-Avoid Verification

In this paper, we study infinite-horizon reach-avoid verification for continuous-time stochastic systems modeled by stochastic differential equations (SDEs). We formulate this problem within a barrier-function-based framework, which transforms the verification problem into an existence problem for barrier functions satisfying barrier-like conditions expressed as functional inequalities. We provide sufficient and necessary barrier-like conditions in terms of polynomial barrier functions for infinite-horizon reach-avoid verification under suitable regularity and uniform ellipticity assumptions. We first construct a discounted value function that characterizes lower bounds on the reach-avoid probability. We then show that it is the unique classical solution of an associated elliptic Dirichlet problem. Based on this characterization, we further show that the barrier-like condition proposed in our previous work on finite-horizon reach-avoid verification is not only sufficient for infinite-horizon reach-avoid verification but also necessary whenever the reach-avoid probability is strictly larger than the specified threshold. In particular, whenever the reach-avoid probability is strictly larger than the specified threshold fro every state in the initial set, polynomial barrier functions satisfying this barrier-like condition exist. Furthermore, when the system dynamics are polynomial, we formulate the problem of finding polynomial barrier functions satisfying this barrier-like condition as sum-of-squares (SOS) programs, which are shown to be sound and complete. Finally, we demonstrate the theoretical results on two numerical examples.

eess.SY↗