Optimal control of differentially flat underactuated planar robots in the perspective of oscillation mitigation

2026-03-16

AI Summary

This study addresses the challenge of residual end-effector oscillations in underactuated planar robots during low-speed trajectory tracking, which arises from difficulties in accurately modeling passive joints. To mitigate this issue, the authors propose a method that integrates differential flatness with optimal control, explicitly incorporating the minimization of passive joint potential energy into a quadratic performance index. By jointly optimizing control torques and potential energy, the approach generates trajectories driven by flat outputs. The resulting control strategy demonstrates robustness to variations in passive joint stiffness and damping parameters, effectively alleviating oscillations caused by model-parameter mismatches. Simulation results confirm that the proposed method significantly suppresses residual oscillations, thereby enhancing both trajectory tracking accuracy and overall system robustness.

Technology Category

Intelligent Robots: Motion and Path PlanningPlanning, Routing, and Scheduling: Replanning and Plan RepairReasoning under Uncertainty: Stochastic Optimization

Application Category

Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environmentsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsResponsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Underactuated robots are characterized by a larger number of degrees of freedom than actuators and if they are designed with a specific mass distribution, they can be controlled by means of differential flatness theory. This structural property enables the development of lightweight and cost-effective robotic systems with enhanced dexterity. However, a key challenge lies in managing the passive joints, whose control demands precise and comprehensive dynamic modeling of the system. To simplify dynamic models, particularly for low-speed trajectories, friction is often neglected. While this assumption simplifies analysis and control design, it introduces residual oscillations of the end-effector about the target position. In this paper, the possibility of using optimal control along with differential flatness control is investigated to improve the tracking of the planned trajectories. First, the study was carried out through formal analysis, and then, it was validated by means of numerical simulations. Results highlight that optimal control can be used to plan the flat variables considering different (quadratic) performance indices: control effort, i.e. motor torque, and potential energy of the considered underactuated joint. Moreover, the minimization of potential energy can be used to design motion laws that are robust against variation of the stiffness and damping of the underactuated joint, thus reducing oscillations in the case of stiffness/damping mismatch.

Problem

• underactuated robots
• oscillation mitigation
• differential flatness
• residual oscillations
• passive joints

Innovation

• optimal control
• differential flatness
• underactuated robots
• oscillation mitigation
• trajectory planning