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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.”
From Learning quadrupedal locomotion over challenging terrain (2020) · cites this paper as [5]
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“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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- 2018, Cassie Blue and Associated Press
- 2018, Cassie Blue at the UM Dental School
- 2018, Cassie Blue Hones Her Segway Riding Skills
- 2018, Cassie Blue Plays in the Sand
- 2018, Cassie Blue Summary Video
- 2018, Cassie Blue Walks Through Fire
- 2019, Cassie’s Polar Vortex Original Record
- 2019, Feedback Controller for a Cassie Robot
- Hartley, 2017, Cassie URDF and FROST Model
- 10.1115/DSCC2015-9899 · DOI
- 2018, Cassie Simulators
- Schepelmann, 2018, Experimental evaluation of robust swing-leg placement controls in robotic limb testbeds
Cited by
Sorted by citations
Learning quadrupedal locomotion over challenging terrain
Lee, J., Hwangbo, J., Wellhausen, L., Koltun, V., & Hutter, M. (2020) · Science Robotics · doi:10.1126/scirobotics.abc5986 · Cited by 1,156
“Many rely on elaborate state machines that coordinate the execution of motion primitives and reflex controllers [1–5].”
Learning quadrupedal locomotion over challenging terrain
Lee, J., Hwangbo, J., Wellhausen, L., Koltun, V., & Hutter, M. (2020) · Repository for Publications and Research Data (ETH Zurich) · doi:10.3929/ethz-b-000448343 · Cited by 752
Contact-aided invariant extended Kalman filtering for robot state estimation
Hartley, R., Ghaffari, M., Eustice, R. M., & Grizzle, J. W. (2020) · The International Journal of Robotics Research · doi:10.1177/0278364919894385 · Cited by 325
Self-citationAdvancements in Humanoid Robots: A Comprehensive Review and Future Prospects
Tong, Y., Liu, H., & Zhang, Z. (2024) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2023.124140 · Cited by 315
Real-world humanoid locomotion with reinforcement learning
Radosavovic, I., Xiao, T., Zhang, B., Darrell, T., Malik, J., & Sreenath, K. (2024) · Science Robotics · doi:10.1126/scirobotics.adi9579 · Cited by 346
Reinforcement Learning for Robust Parameterized Locomotion Control of Bipedal Robots
Li, Z., Cheng, X., Peng, X. B., Abbeel, P., Levine, S., Berseth, G., & Sreenath, K. (2021) · 2021 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra48506.2021.9560769 · Cited by 219
“Model-based methods require careful system identification to bridge the reality gap [16], [17].”
BackgroundMethodReinforcement learning for versatile, dynamic, and robust bipedal locomotion control
Li, Z., Peng, X. B., Abbeel, P., Levine, S., Berseth, G., & Sreenath, K. (2024) · The International Journal of Robotics Research · doi:10.1177/02783649241285161 · Cited by 184
“Their configurations, defined as [kernel size, filter size, stride size], are [6, 32, 3] and [4, 16, 2] with relu activation and no padding, respectively.”
Improvements to Target-Based 3D LiDAR to Camera Calibration
Huang, J.-K., & Grizzle, J. W. (2020) · IEEE Access · doi:10.1109/access.2020.3010734 · Cited by 119
Self-citationLearning Locomotion Skills for Cassie: Iterative Design and Sim-to-Real
Xie, Z., Clary, P., Dao, J., Morais, P., HURST, J. W., & van de Panne, M. (2019) · Conference on Robot Learning · Cited by 114
3-D Underactuated Bipedal Walking via H-LIP Based Gait Synthesis and Stepping Stabilization
Xiong, X., & Ames, A. D. (2022) · IEEE Transactions on Robotics · doi:10.1109/tro.2022.3150219 · Cited by 97
“Compared to the periodic walking realized via HZD [8], [30], [31], the periodic orbits of the H-LIP are directly controlled via the step size on the S2S dynamics.”
BackgroundModel predictive control of legged and humanoid robots: models and algorithms
Katayama, S., Murooka, M., & Tazaki, Y. (2023) · Advanced Robotics · doi:10.1080/01691864.2023.2168134 · Cited by 91
“achievements using hardware platforms, such as theHRP series [6–8], TORO [9], Atlas [10], TALOS [11], E2-DR [12], andCassie [13], have been reported in the literature.”
MethodDynamic Walking: Toward Agile and Efficient Bipedal Robots
Reher, J., & Ames, A. D. (2020) · Annual Review of Control Robotics and Autonomous Systems · doi:10.1146/annurev-control-071020-045021 · Cited by 86
“Dynamic walking on Cassie has been successfully realized on hardware both by planning under the assumption of sufficient rigidity in the legs to ignore compliant elements (118), and for walking which considers the passive compliance in the zero dynamics (119).”
MethodDynamic Walking with Compliance on a Cassie Bipedal Robot
Reher, J., Ma, W.-L., & Ames, A. D. (2019) · 2019 18th European Control Conference (ECC) · doi:10.23919/ecc.2019.8796090 · Cited by 81
“Therefore, certain levels of approximation have been suggested: a gait library method [8] which ignores the compliant dynamics in the robot has demonstrated robust walking behaviors with the addition of several ad-hoc components; a machine learning method [25] has also been used to train control policies on a perturbe…”
BackgroundMethodRobust Feedback Motion Policy Design Using Reinforcement Learning on a 3D Digit Bipedal Robot
Castillo, G. A., Weng, B.-W., Zhang, W., & Hereid, A. (2021) · IEEE/RJS International Conference on Intelligent RObots and Systems · doi:10.1109/iros51168.2021.9636467 · Cited by 79
“The standing controller implemented for Digit is based on the standing controller for Cassie in [21].”
BackgroundMethodSelf-citationAdapting Rapid Motor Adaptation for Bipedal Robots
Kumar, A., Li, Z., Zeng, J., Pathak, D., Sreenath, K., & Malik, J. (2022) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros47612.2022.9981091 · Cited by 86
“We benchmark the ARMA with the following locomotion controllers on Cassie as baselines: 1) a HZD-based controller (HZD) developed in [12] based on [11], 2) a robust RL-based locomotion controller represented by MLP (Robust MLP) developed”
BackgroundMethodIterative Reinforcement Learning Based Design of Dynamic Locomotion Skills for CassiePreprint
Xie, Z., Clary, P., Dao, J., Morais, P., HURST, J. W., & van de Panne, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.09537 · Cited by 80
“To utilize the full dynamics of the robots, offline trajectory optimization such as direct collocation [11] is often used to generate trajectories, and tracking controllers based on quadratic programming [27] or feedback linearization [7] can be designed along these trajectories.”
BackgroundMethodLi, J., & Nguyen, Q. (2021) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc45484.2021.9683500 · Cited by 61
Zero Dynamics, Pendulum Models, and Angular Momentum in Feedback Control of Bipedal Locomotion
Gong, Y., & Grizzle, J. W. (2022) · Journal of Dynamic Systems Measurement and Control · doi:10.1115/1.4055770 · Cited by 61
“This controller provides improved tracking performance over the straight-up PD implementation in [79].”
BackgroundSelf-citationTeng, S., Mueller, M. W., & Sreenath, K. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9561313 · Cited by 60
“The robot is walking over slippery terrain for about 4 meters within 35 seconds with the controller from [9] implemented.”
BackgroundContact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation
Hartley, R., Jadidi, M. G., Grizzle, J. W., & Eustice, R. M. (2018) · Robotics: Science and Systems · doi:10.15607/rss.2018.xiv.050 · Cited by 57
“d when the robot is standing on the ground. The spring deflections are measured by encoders and serve as a binary contact sensor. The controller used for these experiments was developed by Gong et al. [40]. 9.1. Convergence Comparison An experiment was performed where the robot walked forwards at approximately 0:3 m=se…”
MethodInfluentialSelf-citationGong, Y., & Grizzle, J. W. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9560821 · Cited by 55
“The most frequently proposed variables as surrogates for “balance” include Center of Mass (COM) velocity [3]–[7], COM position [8], Capture Point [9], [10], Zero Moment Point [11], [12],”
BackgroundSelf-citationGibson, G., Dosunmu-Ogunbi, O., Gong, Y., et al. (2022) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros47612.2022.9981969 · Cited by 51
“Each leg has seven joints, five of which are actuated while the remaining two are constrained by springs [30].”
BackgroundSelf-citationEfficient Anytime CLF Reactive Planning System for a Bipedal Robot on Undulating Terrain
Huang, J.-K., & Grizzle, J. W. (2023) · IEEE Transactions on Robotics · doi:10.1109/tro.2022.3228713 · Cited by 50
Self-citationTraversing Steep and Granular Martian Analog Slopes with a Dynamic Quadrupedal Robot
Kolvenbach, H., Arm, P., Hampp, E., Dietsche, A., Bickel, V., Sun, B., Meyer, C., & Hutter, M. (2022) · Field Robotics · doi:10.55417/fr.2022030 · Cited by 51
Inertial Measurement Units (IMUs) in Mobile Robots over the Last Five Years: A Review
Samatas, G. G., & Pachidis, T. P. (2022) · Designs · doi:10.3390/designs6010017 · Cited by 51
Whole-body Humanoid Robot Locomotion with Human Reference
Zhang, Q., Cui, P., Yan, D., Sun, J., Duan, Y., Han, G., Zhao, W., Zhang, W., Guo, Y., Zhang, A., et al. (2024) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros58592.2024.10801451 · Cited by 46
“…Optimus [1] and Figure’s humanoid robots 2 have learned from human data to perform complex desktop manipulation tasks; the bipedal robot Cassie [2] [3] [4] and its humanoid version Digit 3 , are powered by motors and successfully move across a variety of terrains; the renowned legged robot…”
Hereid, A., Harib, O., Hartley, R., et al. (2019) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros40897.2019.8968056 · Cited by 43
“0 m/s on flat ground were used to generate a gait library [8], [11] for Cassie Blue to regulate the forward and backward walking speeds.”
MethodSelf-citationCTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotion
Wang, H., Luo, H. L., Zhang, W., & Chen, H. (2024) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2024.3457379 · Cited by 49
Castillo, G. A., Weng, B., Zhang, W., & Hereid, A. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9197175 · Cited by 43
“Foot placement controller has been widely used in 3D bipedal walking robots with the objective of improving the speed tracking and the stability and robustness of the walking gait [17], [19], [28].”
BackgroundMethodInfluentialSelf-citationSakai, R., Katsumata, S., Miki, T., et al. (2019) · Advanced Robotics · doi:10.1080/01691864.2019.1705909 · Cited by 41
Proximal and Sparse Resolution of Constrained Dynamic Equations
Carpentier, J., Budhiraja, R., & Mansard, N. (2021) · Robotics: Science and Systems · doi:10.15607/rss.2021.xvii.017 · Cited by 40
“Cassie robot [19] simulation: Each leg of the robot has two 3D kinematic loop constraints, and line contact with the ground (implemented as 3D constraints at heel and toe).”
Implementation of a Reactive Walking Controller for the New Open-Hardware Quadruped Solo-12
Léziart, P., Flayols, T., Grimminger, F., Mansard, N., & Souères, P. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9561559 · Cited by 37
Inverse Dynamics Control of Compliant Hybrid Zero Dynamic Walking
Reher, J., & Ames, A. D. (2021) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra48506.2021.9560906 · Cited by 36
“In previous work on Cassie [9], [24], PD control achieved reasonable tracking of the desired outputs with the passive compliance in the system matching the planned response.”
BackgroundResultValidating Robotics Simulators on Real-World Impacts
Acosta, B., Yang, W., & Posa, M. (2022) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2022.3174367 · Cited by 36
Compliant Motion Control of Wheel-Legged Humanoid Robot on Rough Terrains
Zhao, L., Yu, Z., Han, L., et al. (2023) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2023.3320762 · Cited by 35
“In recent years, Gong et al. [6], [7] employed the feedback control for standing and walking using virtual constraints meth-ods and gait libraries on Cassie to methodically comprehend walking on sidewalks, grass, and snow.”
MethodAutonomous navigation of underactuated bipedal robots in height-constrained environments
Li, Z., Zeng, J., Chen, S., et al. (2023) · The International Journal of Robotics Research · doi:10.1177/02783649231187670 · Cited by 35
“In experiments, HZD is validated on a range of bipedal robots with point or linear feet in [44]–[46], and more recently, on Cassie in [47]–[49].”
BackgroundInfluentialIntegrated Task and Motion Planning for Safe Legged Navigation in Partially Observable Environments
Shamsah, A., Gu, Z., Warnke, J., et al. (2023) · IEEE Transactions on Robotics · doi:10.1109/tro.2023.3299524 · Cited by 35
“One common feature of popular dynamic controllers [77], [78] for bipedal locomotion is the zero actuation of the ankle actuator (providing zero or a small damping torque to the ankle pitch and roll joints).”
BackgroundNakata, Y., Yagi, S., Yu, S., Wang, Y., Ise, N., Nakamura, Y., & Ishiguro, H. (2021) · Robotica · doi:10.1017/s0263574721000898 · Cited by 31
“As the hardware technologies required for the development of humanoid robots and embedding them in a real environment have advanced considerably [4, 5], the expectations associated with the implementation of such robots in society are rapidly growing.”
BackgroundLinear Policies are Sufficient to Realize Robust Bipedal Walking on Challenging Terrains
Krishna, L., Castillo, G. A., Mishra, U. A., Hereid, A., & Kolathaya, S. (2022) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2022.3143227 · Cited by 30
Self-citationXiong, X., & Ames, A. D. (2019) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros40897.2019.8968162 · Cited by 29
“In other words, the springs on the robot were assumed rigid in [28].”
BackgroundReinforcement Learning-Based Cascade Motion Policy Design for Robust 3D Bipedal Locomotion
Castillo, G. A., Weng, B., Zhang, W., & Hereid, A. (2022) · IEEE Access · doi:10.1109/access.2022.3151771 · Cited by 35
“The swing foot regulations , i.e., δ swhp δ swhr , and δ swhy , are originally inspired by the LIP model and has been applied to improve the stability and robustness of model-based feedback controller for 3D bipedal based on the tracking of the average walking speed [32]–[36].”
BackgroundMethodSelf-citationWang, Y., Chen, T., Rong, X., et al. (2024) · IEEE/ASME Transactions on Mechatronics · doi:10.1109/tmech.2024.3420390 · Cited by 28
“Cassie [10] and ATRIAS [11] are capable of adapting to complex terrains, such as grassy fields and uneven road surfaces.”
Gong, Y., & Grizzle, J. W. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2008.10763 · Cited by 27
“This provided improved tracking performance over the straight-up PD implementation in [9].”
BackgroundSelf-citationImpact Invariant Control with Applications to Bipedal Locomotion
Yang, W., & Posa, M. (2021) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros51168.2021.9636094 · Cited by 26
“These include controller such as Hybrid LQR [7], joint PD control [14] [15], as well as inverse dynamics controllers that primarily track joint space”
Revisiting Reward Design and Evaluation for Robust Humanoid Standing and Walking
Marum, B. V., Shrestha, A., Duan, H., Dugar, P., Dao, J., & Fern, A. (2024) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros58592.2024.10802680 · Cited by 39
“There have been a number of prior approaches for model-based humanoid SaW control [7, 8, 9, 10, 11].”
Animated Cassie: A Dynamic Relatable Robotic Character
Li, Z., Cummings, C., & Sreenath, K. (2020) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros45743.2020.9340894 · Cited by 25
System Design and Balance Control of a Novel Electrically-driven Wheel-legged Humanoid Robot
Zhao, L., Yu, Z., Chen, X., et al. (2021) · IEEE International Conference on Unmanned Systems (ICUS) · doi:10.1109/icus52573.2021.9641385 · Cited by 23
Toward Safety-Aware Informative Motion Planning for Legged RobotsPreprint
Teng, S., Gong, Y., Grizzle, J. W., & Ghaffari, M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.14252 · Cited by 23
“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
“These robots have great potential to be controlled autonomously (e.g., ATRIAS [2], Cassie [3], MIT Cheetah 3 [4], ANYmal quadruped [5], and Boston Dynamics Spot autonomous exploration mission [6]).”
BackgroundFast Online Planning for Bipedal Locomotion via Centroidal Model Predictive Gait Synthesis
Guo, Y., Zhang, M., Dong, H., et al. (2021) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2021.3092268 · Cited by 20
Rough-Terrain Locomotion and Unilateral Contact Force Regulations With a Multi-Modal Legged Robot
Liang, K., Sihite, E. N., Dangol, P., et al. (2021) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc50511.2021.9483189 · Cited by 20
“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 23
“…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
“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 21
Feller, D., & Siemers, C. (2022) · Robotics · doi:10.3390/robotics11020039 · Cited by 18
“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
“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
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
“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
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
“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 19
“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 20
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
“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
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
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 16
“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
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
“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 13
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
“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
“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
“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., Guo, R., Leestma, J. K., Sawicki, G. S., & Zhao, Y. (2025) · IEEE Transactions on Robotics · doi:10.1109/tro.2025.3582820 · Cited by 13
“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
“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
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
“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
“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
“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
“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
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
“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
Bhardwaj, G., Mishra, U. A., Sukavanam, N., & Balasubramanian, R. (2022) · Applied Intelligence · doi:10.1007/s10489-022-03921-6 · Cited by 9
“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
“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
“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
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
“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
“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
Feller, D. (2023) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-023-01900-8 · Cited by 8
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
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
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
Lin, C.-Y. R., & Lee, J.-M. (2023) · Biomimetics · doi:10.3390/biomimetics8020204 · Cited by 7
“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
“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
“[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
“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
“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
“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
Metadata
- 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
- 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 › Control and Systems 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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