Feedback Control of a Cassie Bipedal Robot: Walking, Standing, and Riding a Segway
Open accessAbstract
The Cassie bipedal robot designed by Agility Robotics is providing academics with a common platform for sharing and comparing algorithms for locomotion, perception, and navigation. This paper focuses on feedback control for standing and walking using the methods of virtual constraints and gait libraries. The designed controller was implemented six weeks after the robot arrived at the University of Michigan and allowed it to stand in place as well as walk over sidewalks, grass, snow, sand, and burning brush. The controller for standing also enables the robot to ride a Segway. Software supporting the work in this paper is available on GitHub.
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To date, no published work has demonstrated dynamic locomotion in diverse, challenging natural environments as shown in Fig. 1.
“To date, no published work has demonstrated dynamic locomotion in diverse, challenging natural environments as shown in Fig. 1.”
From Learning quadrupedal locomotion over challenging terrain (2020) · cites this paper as [5]
Conventional controllers for legged locomotion are based on elaborate state machines that explicitly trigger the execution of motion primitives and reflexes.
“Many rely on elaborate state machines that coordinate the execution of motion primitives and reflex controllers [1-5].”
From Learning quadrupedal locomotion over challenging terrain (2020) · cites this paper as [5]
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BackgroundMethodRobust Feedback Motion Policy Design Using Reinforcement Learning on a 3D Digit Bipedal Robot
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Zero Dynamics, Pendulum Models, and Angular Momentum in Feedback Control of Bipedal Locomotion
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Implementation of a Reactive Walking Controller for the New Open-Hardware Quadruped Solo-12
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BackgroundInfluentialIntegrated Task and Motion Planning for Safe Legged Navigation in Partially Observable Environments
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BackgroundLinear Policies are Sufficient to Realize Robust Bipedal Walking on Challenging Terrains
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BackgroundSelf-citationImpact Invariant Control with Applications to Bipedal Locomotion
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Revisiting Reward Design and Evaluation for Robust Humanoid Standing and Walking
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Animated Cassie: A Dynamic Relatable Robotic Character
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System Design and Balance Control of a Novel Electrically-driven Wheel-legged Humanoid Robot
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Toward Safety-Aware Informative Motion Planning for Legged RobotsPreprint
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“Hybrid Zero Dynamics (HZD)-based periodic gait design [30] enables asymptotically stable walking pattern using optimization on the robot full dynamics [31, 32].”
Self-citationBalancing Control and Pose Optimization for wheel-legged Robots Navigating High Obstacles
Li, J., Ma, J., & Nguyen, Q. (2022) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros47612.2022.9981432 · Cited by 23 · see citing works
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BackgroundFast Online Planning for Bipedal Locomotion via Centroidal Model Predictive Gait Synthesis
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Rough-Terrain Locomotion and Unilateral Contact Force Regulations With a Multi-Modal Legged Robot
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“Agility Robotics’ Cassie [3], Honda’s ASIMO [4] and Samsung’s Mahru III [5] are capable of walking, running, dancing and going up and down stairs, and the Yobotics-IHMC [6] biped can recover from pushes.”
BackgroundDo robots outperform humans in human-centered domains?
Riener, R., Rabezzana, L., & Zimmermann, Y. (2023) · Frontiers in Robotics and AI · doi:10.3389/frobt.2023.1223946 · Cited by 19 · see citing works
“…last decade with robots such as Atlas, MIT Cheetah, ANYmal, Spot, or Cassie (Boston Dynamics, 2022; Seok et al., 2014; Hutter et al., 2016a; Boston Dynamics Support Center, 2021; Gong et al., 2019) and its commercially available successor Digit (C et al., 2021; NED Directory, 2023; Robots, 2019).”
BackgroundMethodInfluentialXi, A., & Chen, C. (2020) · IEEE Access · doi:10.1109/access.2020.3015506 · Cited by 19 · see citing works
“Other implementations based on conventional approaches focus on biped walking control on uneven surface, which involves inclined surface [7], partially inclined surface [8], and grass, snow, sand, burning brush [9].”
BackgroundXiong, X., & Ames, A. D. (2020) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros45743.2020.9341467 · Cited by 19 · see citing works
Feller, D., & Siemers, C. (2022) · Robotics · doi:10.3390/robotics11020039 · Cited by 18 · see citing works
“Thus, without completeness, remarkable results have been shown regarding quadrupedal robots such as the Raibert quadruped [1], BigDog [2], Spot (Classic) and SpotMini [3], MIT Cheetah [4], ANYmal [5], HyQ [6], and the two-legged robots Atlas [7], ASIMO [8], ATRIAS [9,10], Cassie [11], and HRP [12].”
Design and control of BRAVER: a bipedal robot actuated via proprioceptive electric motors
Zhu, Z., Zhu, W., Zhang, G., et al. (2023) · Autonomous Robots · doi:10.1007/s10514-023-10117-5 · Cited by 18 · see citing works
“Cassie (Gong et al., 2019; AgilityRobotics, 2022), Digit (AgilityRobotics, 2019), Kan-garoo (Roig et al., 2022), and Atlas (Guizzo, 2019) use the same strategy centering their actuators close to the pelvis to reduce their leg inertia and transfer the motion to their leg through closed-bar linkages.”
BackgroundSoft Foot Sensor Design and Terrain Classification for Dynamic Legged Locomotion
Guo, X., Blaise, B., Molnar, J. L., et al. (2020) · IEEE International Conference on Soft Robotics (RoboSoft) · doi:10.1109/robosoft48309.2020.9115990 · Cited by 18 · see citing works
Upright and Crawling Locomotion and Its Transition for a Wheel-Legged Robot
Qiu, X., Yu, Z., Meng, L., et al. (2022) · Micromachines · doi:10.3390/mi13081252 · Cited by 17 · see citing works
“Wheel-legged robots combine the advantages of wheeled robots and legged robots [8–10], so they can travel efficiently on flat ground with the help of wheels and overcome uneven terrains and obstacles with the help of legs [11–16].”
BackgroundA versatile humanoid robot platform for dexterous manipulation and human–robot collaboration
Shu, X., Ni, F., Fan, X., et al. (2023) · CAAI Transactions on Intelligence Technology · doi:10.1049/cit2.12214 · Cited by 16 · see citing works
Watch the Next Step: A Comprehensive Survey of Stair-Climbing Vehicles
Pappalettera, A., Bottiglione, F., Mantriota, G., & Reina, G. (2023) · Robotics · doi:10.3390/robotics12030074 · Cited by 16 · see citing works
“Cassie [96,97] is the most recent robot of the three listed.”
BackgroundToward Understanding Key Estimation in Learning Robust Humanoid Locomotion
Wang, Z., Wei, W., Yu, R., Wu, J., & Zhu, Q. (2024) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros58592.2024.10801648 · Cited by 16 · see citing works
“Classical control methods can achieve stable static motion [1]–[3], and furthermore, optimization-based strategies can generate dynamic behaviors while adhering to constraints [4]–[7].”
Learning Forward Dynamics Model and Informed Trajectory Sampler for Safe Quadruped Navigation
Kim, Y., Kim, C., & Hwangbo, J. (2022) · Robotics: Science and Systems · doi:10.15607/rss.2022.xviii.069 · Cited by 16 · see citing works
Reactive Locomotion Decision-Making and Robust Motion Planning for Real-Time Perturbation Recovery
Gu, Z., Boyd, N., & Zhao, Y. (2022) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra46639.2022.9812068 · Cited by 15 · see citing works
“Behavior libraries have also been used to generate robust real-time walking in unstructured or constrained environments [10], [11].”
MethodYang, L., Li, Z., Zeng, J., et al. (2022) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra46639.2022.9812154 · Cited by 15 · see citing works
Unilateral Ground Contact Force Regulations in Thruster-Assisted Legged Locomotion
Sihite, E. N., Dangol, P., & Ramezani, A. (2021) · IEEE/ASME International Conference on Advanced Intelligent Mechatronics · doi:10.1109/aim46487.2021.9517648 · Cited by 14 · see citing works
Learning Gait-conditioned Bipedal Locomotion with Motor Adaptation*
Wei, W., Wang, Z., Xie, A., Wu, J., Xiong, R., & Zhu, Q. (2023) · IEEE-RAS International Conference on Humanoid Robots (Humanoids) · doi:10.1109/humanoids57100.2023.10375167 · Cited by 15 · see citing works
“For the CNN, its input channel number, output channel number, kernel size, and stride of each layer are [32, 32, 8, 4], [32, 32, 5, 1], [32, 32, 5, 1].”
BackgroundGalliker, M. Y., Csomay-Shanklin, N., Grandia, R., et al. (2022) · IEEE-RAS International Conference on Humanoid Robots (Humanoids) · doi:10.1109/humanoids53995.2022.10000132 · Cited by 14 · see citing works
Shu, X., Ni, F., Fan, X., Liu, C., Yang, S., Tu, B., & Liu, H. (2023) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2023.3266707 · Cited by 14 · see citing works
“The typical solutions are wheel-legged or biped, with Boston Dynamics’ Handle [1] and Atlas [2], and Agility Robotics’ Cassie [3] as state-of-the-art examples.”
MethodMechanosensory Control of Locomotion in Animals and Robots: Moving Forward
Dallmann, C. J., Dickerson, B. H., Simpson, J. H., Wyart, C., & Jayaram, K. (2023) · Integrative and Comparative Biology · doi:10.1093/icb/icad057 · Cited by 12 · see citing works
Dosunmu-Ogunbi, O., Shrivastava, A., Gibson, G., et al. (2023) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros55552.2023.10342369 · Cited by 13 · see citing works
“In part due to precedent [5], [16], [25] and in part due to the new ALIP model of Sec.”
BackgroundSelf-citationFeedback Control for Autonomous Riding of Hovershoes by a Cassie Bipedal Robot
Chen, S., Rogers, J., Zhang, B., et al. (2019) · IEEE-RAS International Conference on Humanoid Robots (Humanoids) · doi:10.1109/humanoids43949.2019.9336618 · Cited by 13 · see citing works
“Our proposed controller is based on a nominal balancing controller for Cassie from [5].”
MethodGuided Curriculum Learning for Walking Over Complex TerrainPreprint
Tidd, B., Hudson, N., & Cosgun, A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.03848 · Cited by 15 · see citing works
“While classical methods can achieve complex behaviours [Shih, 1999], [Gong et al., 2019], [Xiong and Ames, 2018], they typically require expert tuning, limiting their extension to more challenging conditions.”
Gu, Z., Zhao, Y., Chen, Y., et al. (2025) · IEEE Transactions on Robotics · doi:10.1109/tro.2025.3582820 · Cited by 11 · see citing works
“In contrast, the smooth-operator method exhibits solving times that are not only faster but also more consistent, as indicated by the narrower range between the minimum and maximum solving times, with each solving time typically falling within ± 50% of the median time.”
White, J., Swart, D., & Hubicki, C. M. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9196725 · Cited by 11 · see citing works
“Using control outputs that are kinematically defined, “Cassie Blue” was able to stand on uneven surfaces and walk on a variety of outdoor terrains [25].”
MethodLeg Configuration Analysis and Prototype Design of Biped Robot Based on Spring Mass Model
Che, J., Pan, Y., Wei, Y., et al. (2022) · Actuators · doi:10.3390/act11030075 · Cited by 11 · see citing works
Gait optimization and energy-based stability for biped locomotion using large-scale programming
Xie, Y. H., Gao, C., Zhu, S., Yan, X., Kong, L., Xie, A., Gu, J. J., & Zhang, D. (2023) · Robotica · doi:10.1017/s0263574723000413 · Cited by 11 · see citing works
“The off-line optimization-based gait generation improves the capability of generalization to different locomotion scenarios [38].”
BackgroundDesign Guidelines for Bioinspired Adaptive Foot for Stable Interaction With the Environment
Ranjan, A., Angelini, F., Nanayakkara, T., & Garabini, M. (2023) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2023.3326602 · Cited by 11 · see citing works
“Bipedal robots Tello [52], Cassie [53], and BRUCE [54] have a slimmer shaft-like foot that has similar to a line contact with the ground, and the actuation in roll direction is omitted.”
BackgroundAdaptive Fuzzy Robust Control of a Bionic Mechanical Leg With a High Gain Observer
Liao, L., Li, B., Wang, Y., Xi, Y., Zhang, D., & Gao, L. (2021) · IEEE Access · doi:10.1109/access.2021.3091132 · Cited by 11 · see citing works
“Multi-leg walking robots as one kind of bionic robot, compared with traditional wheeled robots and caterpillar robots, possess flexible movement performance, a powerful obstacle avoidance ability and an excellent terrain adaptability [11], and have become prominent research object, including bipedal robots (the humano…”
BackgroundBeyond Inverted Pendulums: Task-Optimal Simple Models of Legged Locomotion
Chen, Y.-M., Hu, J., & Posa, M. (2024) · IEEE Transactions on Robotics · doi:10.1109/tro.2024.3386390 · Cited by 10 · see citing works
“We note that it is a common practice to fix the duration to ease the problem difficulty of (TO) when dealing with high-dimensional robots[51],[71].”
BackgroundEnhancing speed recovery rapidity in bipedal walking with limited foot area using DCM predictions
Han, L., Chen, X., Yu, Z., et al. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.123858 · Cited by 10 · see citing works
Stability Control of a Biped Robot on a Dynamic Platform Based on Hybrid Reinforcement Learning
Xi, A., & Chen, C. (2020) · Sensors · doi:10.3390/s20164468 · Cited by 10 · see citing works
“Although it works perfectly on NAOs, it is not applicable to Michigan’s Cassie-series robots as the parameters of these robots are completely different [10].”
BackgroundLearning-based locomotion control fusing multimodal perception for a bipedal humanoid robot
Ji, C., Liu, D., Gao, W., & Zhang, S. (2025) · Biomimetic Intelligence and Robotics · doi:10.1016/j.birob.2025.100213 · Cited by 9 · see citing works
Bhardwaj, G., Mishra, U. A., Sukavanam, N., & Balasubramanian, R. (2022) · Applied Intelligence · doi:10.1007/s10489-022-03921-6 · Cited by 9 · see citing works
“Developing planning and control modules have been extensively conducted on legged robots as Model Predictive Control (MPC), with a specific inclination towards quadrupeds [13–17].”
BackgroundCastillo, G. A., Weng, B., Stewart, T. C., Zhang, W., & Hereid, A. (2020) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros45743.2020.9341569 · Cited by 9 · see citing works
“The readers can refer to [2], [11], [17] for additional information about the other regulators.”
BackgroundMethodInfluentialSelf-citationLin, C., Ogata, T., Zhong, Z., et al. (2021) · Applied Sciences · doi:10.3390/app11062872 · Cited by 9 · see citing works
“Some studies have also employed trajectory libraries [27], velocity estimation [28], and real-time control [29].”
BackgroundForce-feedback based Whole-body Stabilizer for Position-Controlled Humanoid Robots
Yang, S., Chen, H., Fu, Z., et al. (2021) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros51168.2021.9636634 · Cited by 9 · see citing works
Single-Leg Forward Hopping via Nonlinear Modes
Calzolari, D., Santina, C. D., Giordano, A., et al. (2022) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc53348.2022.9867538 · Cited by 9 · see citing works
“Many of these works focus on the spring-loaded inverted pendulum (SLIP) model [8], [9], for which robotic implementations also exist [10], [11].”
BackgroundHou, L., Li, B., Liu, W., et al. (2022) · Machines · doi:10.3390/machines10110975 · Cited by 8 · see citing works
“Recent studies have also attempted to combine model-based and model-free approaches, such as learning foothold locations in the task space [23] and combining DRL with HZD to achieve higher-level control objectives [24].”
BackgroundInfluentialEmbodying Quasi-Passive Modal Trotting and Pronking in a Sagittal Elastic Quadruped
Calzolari, D., Santina, C. D., Giordano, A., et al. (2023) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2023.3249631 · Cited by 8 · see citing works
Feller, D. (2023) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-023-01900-8 · Cited by 8 · see citing works
Control Lyapunov Functions for Compliant Hybrid Zero Dynamic WalkingPreprint
Reher, J., & Ames, A. D. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.04241 · Cited by 8 · see citing works
Dynamics Modeling and Motion Simulation of a Segway Robotic Transportation System
Al‐Darraji, I., Kakei, A., Ismaeel, A. G., et al. (2022) · Lecture notes in electrical engineering · doi:10.1007/978-981-19-0252-9_9 · Cited by 7 · see citing works
Engineering morphological development in a robotic bipedal walking problem: An empirical study
Naya-Varela, M., Faíña, A., & Duro, R. J. (2023) · Neurocomputing · doi:10.1016/j.neucom.2023.01.003 · Cited by 7 · see citing works
Lin, C.-Y. R., & Lee, J.-M. (2023) · Biomimetics · doi:10.3390/biomimetics8020204 · Cited by 7 · see citing works
“However, the gaits of brachiation robots must be paired with robust and coordinated ledge grip motions, as dissimilar to multiped robots, which can stand up and continue even after falling down [30], it is impossible for brachiation robots to return to a ledge once they fall.”
BackgroundLegway: Design and Development of a Transformable Wheel-Leg Hybrid robot
Namgung, J., & Cho, B. (2023) · IEEE-RAS International Conference on Humanoid Robots (Humanoids) · doi:10.1109/humanoids57100.2023.10375169 · Cited by 7 · see citing works
“Honda’s ASIMO achieved the first successful running [1], and Cassie and Digit of the Agility Robotics are robust to disturbances, enabling walking on various terrains [2], [3].”
BackgroundWeng, B., Castillo, G. A., Zhang, W., et al. (2022) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros47612.2022.9981359 · Cited by 7 · see citing works
“[2], [3], [4], [5], the authors have presented a series of legged robot locomotion methods, including a hybrid zero dynamics (HZD) [23], [24] inspired reinforcement learning (RL) based controller, referred to as HZDRL, for”
Self-citationHan, Y.-H., & Cho, B. (2023) · IEEE-RAS International Conference on Humanoid Robots (Humanoids) · doi:10.1109/humanoids57100.2023.10375177 · Cited by 6 · see citing works
“Furthermore, the combination of these optimized actuators with an optimal walking design library method [6] has enabled Cassie to achieve efficient and stable walking performance [7].”
MethodWang, X., Guo, W. P., Zhang, T., et al. (2025) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-025-02249-w · Cited by 6 · see citing works
“Except for robots with elastic passive joints like Cassie and Digit, few bipedal robots can use the SLIP model for stable motion control, and validation methods mostly rely on simulations [13–15].”
Load-Carrying Assistance of Articulated Legged Robots Based on Hydrostatic Support
Wu, F., Dai, Z., Li, W., et al. (2024) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2024.3440102 · Cited by 6 · see citing works
“ATRIAS,thepreviousversion ofCassie[19],oneofthemostefficientleggedrobot,hasaCoT of1.”
Fall analysis and prediction for humanoids
Zhang, C., Gao, J., Chen, Z., et al. (2025) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2025.104995 · Cited by 6 · see citing works
- Authors
- Gong, Y., Hartley, R., Da, X., Hereid, A., Harib, O., Huang, J.-K., & Grizzle, J.
- Affiliations
- University of Michigan (US)
- Venue
- 2019 American Control Conference (ACC)
- Publisher
- IEEE
- Published
- 2019-07
- Pages
- 4559-4566
- ISSN
- 0743-1619 (ISSN-L)
- OpenAlex
- W2972798201
- Semantic Scholar
- 76a89e10661d5ccb96af2c76625c24e909ab3b84
- Cited by
- 221
- References
- 26
- Citations by year
- 2026: 9 · 2025: 27 · 2024: 32 · 2023: 48 · 2022: 39 · 2021: 36 · 2020: 19 · 2019: 10 · 2018: 1
- FWCI
- 53.98
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the ... American Control Conference/Proceedings of the American Control Conference (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1525006)
- Toyota Research Institute
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Robotic Locomotion and Control
- Physical Sciences › Engineering › Control and Systems Engineering › Control and Dynamics of Mobile Robots
- Physical Sciences › Engineering › Biomedical Engineering › Prosthetics and Rehabilitation Robotics
- Keywords
- feedback control, virtual constraints, bipedal walking, legged locomotion
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