Numerical Approach for Trajectory Smoothing for LegUp Rehabilitation Parallel Robot

Iosif Birlescu, Vlad Mihaly, Calin Vaida, Andrei Caprariu, Paul Tucan, Jose Machado and Doina Pisla ()
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Iosif Birlescu: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Vlad Mihaly: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Calin Vaida: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Andrei Caprariu: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Paul Tucan: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Jose Machado: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Doina Pisla: CESTER—Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania

Mathematics, 2025, vol. 13, issue 8, 1-23

Abstract: Robotic-assisted motor rehabilitation has seen significant development over the past decade, driven by the distinct advantages that robots offer in this medical task. A key aspect of robotic-assisted rehabilitation is ensuring that the performed rehabilitation exercises are safely planned (i.e., without the risk of patient injury or anatomic joint strain). This paper presents a new numerical approach to trajectory planning for a LegUp parallel robot designed for lower limb rehabilitation. The proposed approach generates S-shaped motion profiles, also called S-curves, with precise control over all kinematic parameters, resulting in smooth acceleration and deceleration. This approach ensures the safety and effectiveness of rehabilitation exercises by minimizing strain on the patient’s anatomical joints. The mathematical models employed (numerical integration and differentiation) are well-established and computationally efficient for real-time implementation in the robot’s control hardware. Experimental tests using LegUp validate the effectiveness of the proposed trajectory-smoothing approach.

Keywords: parallel robot; numerical methods; lower limb rehabilitation; trajectory smoothing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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