Model Predictive Impedance Control and Gait Optimization for High-Speed Quadrupedal Running
Source abstract
Abstract
Controlling legged robots to run at high speeds or to traverse complex terrains remains challenging due to the difficulty of handling the interaction between the robot and the ground. Impedance control and model predictive control are widely used to account for ground reaction forces (GRFs) during dynamic locomotion. This paper introduces a model predictive impedance control (MPIC) method that combines the advantages of both strategies and applies it to a quadruped robot. The proposed approach reformulates MPIC within the single rigid body model (SRBM) framework and derives linear inequality constraints for the equivalent wrench, allowing explicit consideration of GRF limits while retaining compliant behavior against ground impacts and external disturbances. Furthermore, a novel optimized gait pattern based on a simplified dynamic model is introduced to minimize the effect of GRFs on the robot. The resulting gait improves stability compared to conventional gait patterns while maintaining a similar level of energy efficiency. The proposed method is validated through various simulations under diverse conditions. The results demonstrate that it enables the quadruped robot to run at a speed of 12 m/s while maintaining stability against repeated lateral disturbances.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Robotic Locomotion and Control · Prosthetics and Rehabilitation Robotics · Neurogenetic and Muscular Disorders Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mechanical Engineering, Hanyang University, Seoul 04763, Republic of Korea
Korea Institute of Industrial Technology (KITECH), Ansan 15588, Republic of Korea
Funding
Ministry of Trade, Industry and Energy (MOTIE)
References (63)
Show source-provided references
1. High-speed bounding with the MIT Cheetah 2: Control design and experiments10.1177/0278364917694244 ↗
2. Reduced Model Predictive Control Toward Highly Dynamic Quadruped Locomotion10.1109/ACCESS.2024.3360479 ↗
3. Pratt, J.E., and Pratt, G.A. (1997, January 20–25). Virtual model control of a biped walking robot. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Albuquerque, NM, USA.
4. Impedance control for biped robot locomotion10.1109/70.976014 ↗
5. Balance and impedance control for biped humanoid robot locomotion
6. Focchi, M., Boaventura, T., Semini, C., Frigerio, M., Buchli, J., and Caldwell, D.G. (2012, January 25–27). Torque-control based compliant actuation of a quadruped robot. Proceedings of the 2012 12th IEEE International Workshop on Advanced Motion Control (AMC), Sarajevo, Bosnia and Herzegovina.10.1109/AMC.2012.6197133 ↗
7. Boaventura, T., Medrano-Cerda, G.A., Semini, C., Buchli, J., and Caldwell, D.G. (2013, January 3–7). Stability and performance of the compliance controller of the quadruped robot HyQ. Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan.10.1109/IROS.2013.6696541 ↗
8. Model-based hydraulic impedance control for dynamic robots10.1109/TRO.2015.2482061 ↗
9. Towards versatile legged robots through active impedance control10.1177/0278364915578839 ↗
10. High speed trot-running: Implementation of a hierarchical controller using proprioceptive impedance control on the MIT Cheetah10.1177/0278364914532150 ↗
11. Lee, J., Hyun, D.J., Ahn, J., Kim, S., and Hogan, N. (2014, January 14–18). On the dynamics of a quadruped robot model with impedance control: Self-stabilizing high speed trot-running and period-doubling bifurcations. Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, USA.10.1109/IROS.2014.6943260 ↗
12. Bosworth, W., Kim, S., and Hogan, N. (2014, January 14–18). The effect of leg impedance on stability and efficiency in quadrupedal trotting. Proceedings of the 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL, USA.10.1109/IROS.2014.6943258 ↗
13. Park, J., and Park, J.H. (2012, January 7–12). Impedance control of quadruped robot and its impedance characteristic modulation for trotting on irregular terrain. Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, Algarve, Portugal.10.1109/IROS.2012.6385710 ↗
14. Ajallooeian, M., Pouya, S., Spröwitz, A., and Ijspeert, A.J. (2013, January 6–10). Central pattern generators augmented with virtual model control for quadruped rough terrain locomotion. Proceedings of the 2013 IEEE International Conference on Robotics and Automation, Karlsruhe, Germany.10.1109/ICRA.2013.6631040 ↗
15. Torso motion control and toe trajectory generation of a trotting quadruped robot based on virtual model control10.1080/01691864.2015.1113889 ↗
16. Virtual model control for quadruped robots
17. Angelini, F., Xin, G., Wolfslag, W.J., Tiseo, C., Mistry, M., Garabini, M., Bicchi, A., and Vijayakumar, S. (2019, January 4–8). Online optimal impedance planning for legged robots. Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China.10.1109/IROS40897.2019.8967696 ↗
18. Xin, G., Wolfslag, W., Lin, H.C., Tiseo, C., and Mistry, M. (2020). An Optimization-Based Locomotion Controller for Quadruped Robots Leveraging Cartesian Impedance Control. Front. Robot. AI, 7.10.3389/frobt.2020.00048 ↗
19. Towards Generation and Transition of Diverse Gaits for Quadrupedal Robots Based on Trajectory Optimization and Whole-Body Impedance Control10.1109/LRA.2023.3251184 ↗
20. Pedro, G.D.G., Bermudez, G., Medeiros, V.S., Cruz Neto, H.J.d., Barros, L.G.D.d., Pessin, G., Becker, M., Freitas, G.M., and Boaventura, T. (2024). Quadruped Robot Control: An Approach Using Body Planar Motion Control, Legs Impedance Control and Bézier Curves. Sensors, 24.10.3390/s24123825 ↗
21. Parosi, R., Risiglione, M., Caldwell, D.G., Semini, C., and Barasuol, V. (2023, January 1–5). Kinematically-Decoupled Impedance Control for Fast Object Visual Servoing and Grasping on Quadruped Manipulators. Proceedings of the 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Detroit, MI, USA.10.1109/IROS55552.2023.10341714 ↗
22. Bellicoso, C.D., Jenelten, F., Fankhauser, P., Gehring, C., Hwangbo, J., and Hutter, M. (2017, January 24–28). Dynamic Locomotion and Whole-Body Control for Quadrupedal Robots. Proceedings of the 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.
23. Dynamic locomotion through online nonlinear motion optimization for quadrupedal robots10.1109/LRA.2018.2794620 ↗
24. Liu, X., Ma, H., Lang, L., and An, H. (2021). Online Foot Location Planning for Gait Transitioning Using Model Predictive Control. Appl. Sci., 11.10.3390/app11177866 ↗
25. Xin, S., Orsolino, R., and Tsagarakis, N. (2019, January 4–8). Online Relative Footstep Optimization for Legged Robots Dynamic Walking Using Discrete-Time Model Predictive Control. Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China.10.1109/IROS40897.2019.8968028 ↗
26. An MPC-based two-dimensional push recovery of a quadruped robot in trotting gait using its reduced virtual model10.1016/j.mechmachtheory.2019.103737 ↗
27. Whole-body nonlinear model predictive control through contacts for quadrupeds10.1109/LRA.2018.2800124 ↗
28. Model hierarchy predictive control of robotic systems10.1109/LRA.2021.3061322 ↗
29. Bledt, G., Wensing, P.M., and Kim, S. (2017, January 24–28). Policy-regularized model predictive control to stabilize diverse quadrupedal gaits for the MIT cheetah. Proceedings of the 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.10.1109/IROS.2017.8206268 ↗
30. Farshidian, F., Jelavic, E., Satapathy, A., Giftthaler, M., and Buchli, J. (2017, January 15–17). Real-time motion planning of legged robots: A model predictive control approach. Proceedings of the 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids), Birmingham, UK.10.1109/HUMANOIDS.2017.8246930 ↗
31. Bledt, G., and Kim, S. (August, January 31). Extracting legged locomotion heuristics with regularized predictive control. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.10.1109/ICRA40945.2020.9197488 ↗
32. Cebe, O., Tiseo, C., Xin, G., Lin, H.c., Smith, J., and Mistry, M. (June, January 30). Online dynamic trajectory optimization and control for a quadruped robot. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China.10.1109/ICRA48506.2021.9561592 ↗
33. Farshidian, F., Neunert, M., Winkler, A.W., Rey, G., and Buchli, J. (June, January 29). An efficient optimal planning and control framework for quadrupedal locomotion. Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore.10.1109/ICRA.2017.7989016 ↗
34. Bledt, G., Kim, D., Wensing, P.M., and Kim, S. (2018, January 1–5). Dynamic locomotion in the MIT cheetah 3 through convex model-predictive control. Proceedings of the 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.
35. Kim, D., Di Carlo, J., Katz, B., Bledt, G., and Kim, S. (2019). Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control. arXiv.
36. Katz, B., Di Carlo, J., and Kim, S. (2019, January 20–24). Mini cheetah: A platform for pushing the limits of dynamic quadruped control. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.10.1109/ICRA.2019.8793865 ↗
37. Ding, Y., Pandala, A., and Park, H.W. (2019, January 20–24). Real-time model predictive control for versatile dynamic motions in quadrupedal robots. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.10.1109/ICRA.2019.8793669 ↗
38. Representation-free model predictive control for dynamic motions in quadrupeds10.1109/TRO.2020.3046415 ↗
39. Variational-based optimal control of underactuated balancing for dynamic quadrupeds10.1109/ACCESS.2020.2980446 ↗
40. Chignoli, M., and Kim, S. (June, January 30). Online trajectory optimization for dynamic aerial motions of a quadruped robot. Proceedings of the 2021 IEEE International Conference on Robotics and Automation (ICRA), Xi’an, China.10.1109/ICRA48506.2021.9560855 ↗
41. Villarreal, O., Barasuol, V., Wensing, P.M., Caldwell, D.G., and Semini, C. (August, January 31). MPC-based controller with terrain insight for dynamic legged locomotion. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.10.1109/ICRA40945.2020.9197312 ↗
42. A novel dynamic locomotion control method for quadruped robots running on rough terrains10.1109/ACCESS.2020.3016312 ↗
43. Zhang, Z., Chang, X., Ma, H., An, H., and Lang, L. (2023). Model Predictive Control of Quadruped Robot Based on Reinforcement Learning. Appl. Sci., 13.10.3390/app13010154 ↗
44. The gaits of bipedal and quadrupedal animals10.1177/027836498400300205 ↗
45. Optimization and gaits in the locomotion of vertebrates10.1152/physrev.1989.69.4.1199 ↗
46. Steady locomotion in dogs: Temporal and associated spatial coordination patterns and the effect of speed10.1242/jeb.008243 ↗
47. Treadmill locomotion of the mouse lemur (Microcebus murinus); kinematic parameters during symmetrical and asymmetrical gaits10.1007/s00359-018-1256-2 ↗
48. On the stability properties of quadruped creeping gaits10.1016/0025-5564(68)90090-4 ↗
49. A study of the gait control of a quadruped walking vehicle10.1109/JRA.1986.1087040 ↗
50. Investigating stability outcomes across diverse gait patterns in quadruped robots: A comparative analysis10.1109/LRA.2023.3338064 ↗
51. Energy-optimal gait analysis of quadruped robots10.1007/BF02481325 ↗
52. Selecting gaits for economical locomotion of legged robots10.1177/0278364915612572 ↗
53. Pepe, G., Laurenza, M., Belfiore, N.P., and Carcaterra, A. (2021). Quadrupedal robots’ gaits identification via contact forces optimization. Appl. Sci., 11.10.3390/app11052102 ↗
54. Tsujita, K., Tsuchiya, K., and Onat, A. (November, January 29). Adaptive gait pattern control of a quadruped locomotion robot. Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, HI, USA.
55. Fukuoka, Y., Habu, Y., and Fukui, T. (2015). A simple rule for quadrupedal gait generation determined by leg loading feedback: A modeling study. Sci. Rep., 5.10.1038/srep08169 ↗
56. Owaki, D., and Ishiguro, A. (2017). A quadruped robot exhibiting spontaneous gait transitions from walking to trotting to galloping. Sci. Rep., 7.10.1038/s41598-017-00348-9 ↗
57. Learning free gait transition for quadruped robots via phase-guided controller10.1109/LRA.2021.3136645 ↗
58. Bellegarda, G., Shafiee, M., and Ijspeert, A. (2024). AllGaits: Learning all quadruped gaits and transitions. arXiv.
59. Footstep reward for energy-efficient quadruped gait generation and transition through deep reinforcement learning10.1080/01691864.2024.2442718 ↗
60. Bednarczyk, M., Omran, H., and Bayle, B. (August, January 31). Model predictive impedance control. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.10.1109/ICRA40945.2020.9196969 ↗
61. Model predictive variable impedance control of manipulators for adaptive precision-compliance tradeoff10.1109/TMECH.2022.3204350 ↗
62. Centroidal dynamics of a humanoid robot10.1007/s10514-013-9341-4 ↗
63. Todorov, E., Erez, T., and Tassa, Y. (2012, January 7–12). Mujoco: A physics engine for model-based control. Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, Algarve, Portugal.10.1109/IROS.2012.6386109 ↗