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1. Implementation of Deep Deterministic Policy Gradients for Controlling Dynamic Bipedal Walking

   https://doi.org/10.1007/978-3-319-95972-6_29  

   Liu, Chujun; Lonsberry, Andrew G.; Nandor, Mark J.; Audu, Musa L.; Quinn, Roger D. (July 2018, Living Machines: Conference on Biomimetic and Biohybrid Systems)

   A control system for simulated two-dimensional bipedal walking was developed. The biped model was built based on anthropometric data. At the core of the control is a Deep Deterministic Policy Gradients (DDPG) neural network that is trained in GAZEBO, a physics simulator, to predict the ideal foot location to maintain stable walking under external impulse load. Additional controllers for hip joint movement during stance phase, and ankle joint torque during toeoff, help to stabilize the robot during walking. The simulated robot can walk at a steady pace of approximately 1m/s, and during locomotion it can maintain stability with a 30N-s impulse applied at the torso. This work implement DDPG algorithm to solve biped walking control problem. The complexity of DDPG network is decreased through carefully selected state variables and distributed control system. 

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2. Neural Networks Trained via Reinforcement Learning Stabilize Walking of a Three-Dimensional Biped Model With Exoskeleton Applications

   https://doi.org/10.3389/frobt.2021.710999  

   Liu, Chujun; Audu, Musa L.; Triolo, Ronald J.; Quinn, Roger D. (August 2021, Frontiers in Robotics and AI)

   null (Ed.)

   Our group is developing a cyber-physical walking system (CPWS) for people paralyzed by spinal cord injuries (SCI). The current CPWS consists of a functional neuromuscular stimulation (FNS) system and a powered lower-limb exoskeleton for walking with leg movements in the sagittal plane. We are developing neural control systems that learn to assist the user of this CPWS to walk with stability. In a previous publication (Liu et al., Biomimetics, 2019, 4, 28), we showed a neural controller that stabilized a simulated biped in the sagittal plane. We are considering adding degrees of freedom to the CPWS to allow more natural walking movements and improved stability. Thus, in this paper, we present a new neural network enhanced control system that stabilizes a three-dimensional simulated biped model of a human wearing an exoskeleton. Results show that it stabilizes human/exoskeleton models and is robust to impact disturbances. The simulated biped walks at a steady pace in a range of typical human ambulatory speeds from 0.7 to 1.3 m/s, follows waypoints at a precision of 0.3 m, remains stable, and continues walking forward despite impact disturbances and adapts its speed to compensate for persistent external disturbances. Furthermore, the neural network controller stabilizes human models of different statures from 1.4 to 2.2 m tall without any changes to the control parameters. Please see videos at the following link: 3D biped walking control . 

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3. Impact-Free Gaits for Planar Bipeds: Changing Walking Speed and Gait

   Khandelwal, A; Kant, N; Mukherjee, R (October 2024, 2024 4th Modeling, Estimation and Control Conference)

   The problems of changing the walking speed and stride length of impact-free gaits for point-foot planar bipeds are addressed. The impact-free gaits are designed using an approach developed in prior work. It is shown that the impulse controlled Poincar´e map (ICPM) approach can be modified to transition between orbits defining gaits with different walking speeds, and the continuous controller can be changed during the swing phase to transition between gaits that have distinct stride lengths. The effectiveness of the approaches is demonstrated using simulations carried out on a five-link biped. 

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4. Zippy: The smallest power-autonomous bipedal robot

   Man, Steven; Narita, Soma; Macera, Josef; Oke, Naomi; Johnson, Aaron M; Bergbreiter, Sarah (May 2025, IEEE International Conference on Robotics and Automation)

   Miniaturizing legged robot platforms is challenging due to hardware limitations that constrain the number, power density, and precision of actuators at that size. By leveraging design principles of quasi-passive walking robots at any scale, stable locomotion and steering can be achieved with simple mechanisms and open-loop control. Here, we present the design and control of "Zippy", the smallest self-contained bipedal walking robot at only 3.6 cm tall. Zippy has rounded feet, a single motor without feedback control, and is capable of turning, skipping, and ascending steps. At its fastest pace, the robot achieves a forward walking speed of 25 cm/s, which is10 leg lengths per second, the fastest biped robot of any size by that metric. This work explores the design and performance of the robot and compares it to similar dynamic walking robots at larger scales. 

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5. Zippy: The smallest power-autonomous bipedal robot

   Man, Steven; Narita, Soma; Macera, Josef; Oke, Naomi; Johnson, Aaron M; Bergbreiter, Sarah (May 2025, IEEE International Conference on Robotics and Automation)

   Miniaturizing legged robot platforms is challenging due to hardware limitations that constrain the number, power density, and precision of actuators at that size. By leveraging design principles of quasi-passive walking robots at any scale, stable locomotion and steering can be achieved with simple mechanisms and open-loop control. Here, we present the design and control of “Zippy”, the smallest self-contained bipedal walking robot at only 3.6 cm tall. Zippy has rounded feet, a single motor without feedback control, and is capable of turning, skipping, and ascending steps. At its fastest pace, the robot achieves a forward walking speed of 25 cm/s, which is10 leg lengths per second, the fastest biped robot of any size by that metric. This work explores the design and performance of the robot and compares it to similar dynamic walking robots at larger scales. 

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