Üç 3R Robot Kolu ile İşbirlikçi Yük Manipülasyonu: Sanal Empedans Kontrolü Altında Lotka-Volterra Ekolojik Dinamikleri Aracılığıyla Ortaya Çıkan Kuvvet Paylaşımı

Öz

Bu makale, ortak bir yük etrafında simetrik olarak düzenlenmiş üç adet 3R seri robot kolu kullanarak işbirlikçi yük manipülasyonu için yeni bir kontrol mimarisi sunmaktadır. Bu makalenin mevcut literatüre en önemli katkısı, kuvvet paylaşım mekanizması olarak rekabetçi bir ekolojik modelin kullanılmasıdır. Bu yaklaşımda, her robot ortak bir kaynak için rekabet eden bir tür olarak ele alınır ve türler arası etkileşim matrisi, 150 N'luk toplam yükün her an üç ajan arasında nasıl dağıtılacağını yönetir. Lotka-Volterra dinamikleri, ortaya çıkan bir yük yörüngesi P(t)'nin net uç efektör kuvvetleri tarafından yönlendirilen bir kütle-sönümleyici denklemine göre evrimleştiği sanal bir empedans katmanına beslenir. Eklem yörüngeleri, her zaman adımında üstel hareketli ortalama sıcak başlangıçlı bir Jacobian ters kinematik çözücü aracılığıyla çözülür ve Lotka-Volterra çıkışındaki bir alçak geçiş filtresi geçici salınımları bastırır. Sonuç olarak, yükün uzamsal yörüngesinin önceden belirlenmediği, ancak kolektif kuvvet dinamiklerinden ortaya çıktığı tamamen kapalı döngülü bir sistem elde edilir. Mimarinin temel bir özelliği, kendi kendini düzenleyen bozulma iyileşmesidir: t = 12 s ve t = 14 s arasında baskın robotun etkin kuvvet katkısını azaltan sigmoid eğimli bir bozulma olduğunda, ekolojik rekabet, herhangi bir açık yeniden planlama veya denetleyici müdahale olmaksızın, yükü kalan ajanlar arasında doğal olarak yeniden dağıtır. Bu kendi kendini düzenleyen davranış, doğrudan Lotka-Volterra dengesinin limit döngü yapısından kaynaklanır.

Anahtar Kelimeler

• Çoklu robot koordinasyonu
• İşbirlikçi yük manipülasyonu
• Lotka-Volterra modeli
• Kendi kendini düzenleyen bozulma giderme
• Çoklu ajan kuvvet paylaşımı

Destekleyen Kurum

Trakya Üniversitesi

Proje Numarası

2021/131

Cooperative Load Manipulation with Three 3R Robot Arms: Emergent Force Sharing via Lotka–Volterra Ecological Dynamics Under Virtual Impedance Control

Öz

This paper presents a novel control architecture for cooperative load manipulation using three 3R serial robot arms arranged symmetrically around a shared payload. The major contribution of this paper to existing literature is the use of a competitive ecological model as the force-sharing mechanism. In this approach, each robot is treated as a species competing for a common resource, and the inter-species interaction matrix governs how the 150 N total load is distributed among the three agents at every instant. The Lotka-Volterra dynamics feed into a virtual impedance layer in which an emergent load trajectory P(t) evolves according to a mass–damper equation driven by the net end-effector forces. Joint trajectories are resolved at each time step through a Jacobian inverse kinematics solver with exponential moving average warm-start, and a low-pass filter on the Lotka-Volterra output suppresses transient oscillations. The result is a fully closed-loop system in which the load’s spatial trajectory is not prescribed but emerges from the collective force dynamics. A key property of the architecture is its self-regulated disturbance recovery: when a sigmoid-ramped perturbation reduces the dominant robot’s effective force contribution between t = 12 s and t = 14 s, the ecological competition naturally redistributes load across the remaining agents without any explicit re-planning or supervisory intervention. This self-regulating behavior arises directly from the limit-cycle structure of the Lotka-Volterra equilibrium.

Anahtar Kelimeler

• Multi-robot coordination
• Cooperative load manipulation
• Lotka-Volterra model
• Self-regulated disturbance recovery
• Multi-agent force sharing

Destekleyen Kurum

Trakya University

Proje Numarası

2021/131

Kaynakça

1. Balch, T., & Arkin, R. C. (1998). Behavior-based formation control for multirobot teams. IEEE Transactions on Robotics and Automation, 14(6), 926-939. https://doi.org/10.1109/70.736776
2. Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41. https://doi.org/10.1007/s11721-012-0075-2
3. Breazeal, C. (2002). Designing sociable robots. MIT Press.
4. Camarillo, D. B., Krummel, T. M., & Salisbury, J. K., Jr. (2004). Robotic technology in surgery: past, present, and future. American Journal of Surgery, 188(4A Suppl), 2S–15S. https://doi.org/10.1016/j.amjsurg.2004.08.025
5. Culbertson, P., & Schwager, M. (2018). Decentralized Adaptive Control for Collaborative Manipulation. Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA) (pp. 278–285). https://doi.org/10.1109/ICRA.2018.8461263
6. De Schutter, J., & Van Brussel, H. (1988). Compliant robot motion I. A formalism for specifying compliant motion tasks. The International Journal of Robotics Research, 7(4), 3–17. https://doi.org/10.1177/027836498800700401
7. Hofbauer, J., & Sigmund, K. (1998). Evolutionary games and population dynamics. Cambridge University Press.
8. Hogan, N. (1985). Impedance control: An approach to manipulation: Part I—Theory. Journal of Dynamic Systems, Measurement, and Control, 107(1), 1–7. https://doi.org/10.1115/1.3140702

9. Holland, J. H. (1992). Adaptation in natural and artificial systems. MIT Press.
10. Kober, J., Bagnell, J. A., & Peters, J. (2013). Reinforcement learning in robotics: A survey. The International Journal of Robotics Research, 32(11), 1238–1274. https://doi.org/10.1177/0278364913495721
11. Kosuge, K., Oosumi, T., & Chiba, T. (1997). Decentralized control of multiple manipulators handling an object in coordination based on impedance control of each arm. Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97, 1, 17-22. https://doi.org/10.1109/IROS.1997.648976
12. Liu, Y., Passino, K. M., & Polycarpou, M. M. (2003). Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology. IEEE Transactions on Automatic Control, 48(1), 76–95. http://dx.doi.org/10.1109/TAC.2002.806657
13. Lotka, A. J. (1925). Elements of physical biology. Williams & Wilkins Company.
14. Lynch, K. M., & Park, F. C. (2017). Modern robotics: Mechanics, planning, and control. Cambridge University Press.
15. Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE, 95(1), 215–233. https://doi.org/10.1109/JPROC.2006.887293
16. Ott, C., Mukherjee, R., & Nakamura, Y. (2010). Unified impedance and admittance control. Proceedings of the IEEE International Conference on Robotics and Automation, 554–561. https://doi.org/10.1109/ROBOT.2010.5509681
17. Pfeifer, R., & Bongard, J. (2006). How the body shapes the way we think: A new view of intelligence. MIT Press.
18. Raibert, M. H., & Craig, J. J. (1981). Hybrid position/force control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 103(2), 126–133. https://doi.org/10.1115/1.3139652
19. Siciliano, B., & Khatib, O. (2016). Springer handbook of robotics (2nd ed.). Springer. https://doi.org/10.1007/978-3-319-32552-1
20. Sun, Y., & Han, Y. (2025). Analyzing the Impact of Information Asymmetry on Strategy Adaptation in Swarm Robotics: A Game-Theoretic Approach. Symmetry, 17(2), 248. https://doi.org/10.3390/sym17020248
21. Şahin, E. (2005). Swarm robotics: From sources of inspiration to domains of application. In E. Şahin & W. Spears (Eds.), Swarm robotics (pp. 10–20). Springer. https://doi.org/10.1007/978-3-540-30552-1_2
22. Volterra, V. (1926). Variations and fluctuations of the number of individuals in animal species living together. In R. N. Chapman (Ed.), Animal ecology (pp. 409–448). McGraw-Hill.
23. Whitney, D. E. (1969). Resolved motion rate control of manipulators and human prostheses. IEEE Transactions on Man-Machine Systems, 10(2), 47–53. https://doi.org/10.1109/TMMS.1969.299896