University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 Convex optimization approach for the path-following problem of two collaborative robots 471 487 9222 10.22124/jmm.2025.31212.2798 EN Maryam Kia-Lashgami Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. Mohammad Keyanpour Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran. Journal Article 2025 07 19 This paper investigates the time-optimal path-tracking problem for a collaborative robotic system, considering some limitations and dynamic characteristics. This problem is formulated for a robotic system consisting of two-link planar manipulators with and without bar cases along a predetermined geometric path in minimum time. The main challenges are to satisfy both the co-position and co-time conditions of the end-effector movement, as well as the physical limitations of the applied torque to the joints. Through discretization and convexification, we convert the problem into a convex cone optimization problem. The numerical example confirms the effectiveness of the method. https://jmm.guilan.ac.ir/article_9222_b482a06a3e5d0e335f0284dbeb87add2.pdf