Trapezoidal velocity profile with arbitrary initial and final velocities in the problem of controlling a robotic manipulator

Trapezoidal velocity profile with arbitrary initial and final velocities in the problem of controlling a robotic manipulator

Sergey D. Borisov, Master’s Degree, Federal State Autonomous Educational Institution of Higher Education «Bauman Moscow State Technical University» (BMSTU), faculty «Robotics and complex automation» (RK), CAD Systems department (RK6), 5, 2-ya Baumanskaya ul., Moscow, 105005, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it.

Alexander P. Sokolov, Doctor of Engineering Sciences, Professor of CAD Systems department, BMSTU, faculty «Robotics and complex automation» (RK), CAD Systems department (RK6), 5, 2-ya Baumanskaya ul., Moscow, 105005, Russia, This email address is being protected from spambots. You need JavaScript enabled to view it., ORCID: 0000-0002-8930-2536

UDC identifier: 621.865.8:62-50

EDN: NNXLVV

Abstract. In the problem of moving a robotic manipulator through a sequence of given configurations, a situation often arises where approaching a target configuration must occur at a strictly specified velocity. To implement such behavior, a motion law defined by a velocity profile function must be specified for each robot joint, accounting for non-zero initial and final velocities. This work provides an overview of methods for defining velocity profile functions in robotic manipulator control. An improved approach for determining a trapezoidal velocity profile function, considering given initial and final velocities, is proposed. A method for determining the optimal motion duration under kinematic constraints is discussed. Analytical expressions for determining the parameters of the velocity profile function for an arbitrary motion time are presented. A comparison is made between the proposed enhanced velocity profile and alternative methods of defining the velocity profile function. The characteristics and correctness of the proposed method are verified through computational experiments and experimental testing using a robotic manipulator.

Key words: robotic manipulator control, trapezoidal velocity profile, position functions, velocity functions, movement with initial and final velocities

For citation: Borisov, S.D. and Sokolov, A.P. (2026), "Trapezoidal velocity profile with arbitrary initial and final velocities in the problem of controlling a robotic manipulator", Robotics and Technical Cybernetics, vol. 14, no. 1, pp. 30-39,
EDN: NNXLVV. (in Russian).

Acknowledgements
The authors would like to thank the specialists at RoboPro for the opportunity to conduct experimental testing using the RC-10 robotic manipulator, developed by Rozum Robotics in collaboration with RoboPro.

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Received 19.04.2025
Revised 25.09.2025
Accepted 19.11.2025