Wanchao Chi
Research Subjects
Wanchao Chi has a total of 63 co-authors. Here are the top co-authors by number of shared publications:
Chong Zhang
Tencent RoboticsX, Shenzhen, China
6 shared publicationsShenghao Zhang
Tencent Robotics X Lab, Shenzhen, China
6 shared publications- Junzhi Yu
Peking University
5 shared publications - Shihan Kong
Peking University
5 shared publications - Qiuguo Zhu
Zhejiang University
3 shared publications - Yan Meng
State Key Laboratory for Turbulence and Complex Systems, Department of Advanced Manufacturing and Robotics, College of Engineering, Peking University, Beijing 100871, China
3 shared publications
Latest Publications
- 24 November 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Robotics and Automation Letters
- Vol. 11  (2) , 1042-1049
Whole-Body Impedance Coordinative Control for a Wheel-Legged Robot on Uncertain Terrain
This article proposes a whole-body impedance coordinative control framework for a wheel-legged humanoid robot to achieve adaptability on complex terrains while maintaining the robot’s upper body stability. The framework contains a bi-level control strategy. The outer level is a variable-damping impedance controller, which optimizes the damping parameters to ensure the stability of the upper body while holding an object. The inner level employs whole-body control (WBC) optimization that integrates real-time terrain estimation based on wheel-foot position and force data. It generates motor torques while accounting for dynamic constraints, joint limits, friction cones, real-time terrain updates, and a model-free friction compensation strategy. The proposed whole-body coordinative control method, tested on a newly developed quadruped humanoid robot, effectively enables passive stable manipulation for both indoor water-carrying and outdoor box-carrying tasks across varying and uneven terrains.
- 24 November 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Robotics and Automation Letters
- Vol. 11  (2) , 1042-1049
Whole-Body Impedance Coordinative Control for a Wheel-Legged Robot on Uncertain Terrain
This article proposes a whole-body impedance coordinative control framework for a wheel-legged humanoid robot to achieve adaptability on complex terrains while maintaining the robot’s upper body stability. The framework contains a bi-level control strategy. The outer level is a variable-damping impedance controller, which optimizes the damping parameters to ensure the stability of the upper body while holding an object. The inner level employs whole-body control (WBC) optimization that integrates real-time terrain estimation based on wheel-foot position and force data. It generates motor torques while accounting for dynamic constraints, joint limits, friction cones, real-time terrain updates, and a model-free friction compensation strategy. The proposed whole-body coordinative control method, tested on a newly developed quadruped humanoid robot, effectively enables passive stable manipulation for both indoor water-carrying and outdoor box-carrying tasks across varying and uneven terrains.
- Open Access
A Novel ViDAR Device With Visual Inertial Encoder Odometry and Reinforcement Learning-Based Active SLAM Method
In the field of multi-sensor fusion for simultaneous localization and mapping (SLAM), monocular cameras and IMUs are widely used to build simple and effective visual-inertial systems. However, limited research has explored the integration of motor-encoder devices to enhance SLAM performance. By incorporating such devices, it is possible to significantly improve active capability and field of view (FOV) with minimal additional cost and structural complexity. This paper proposes a novel visual-inertial-encoder tightly coupled odometry (VIEO) based on a ViDAR (Video Detection and Ranging) device. A ViDAR calibration method is introduced to ensure accurate initialization for VIEO. In addition, a platform motion decoupled active SLAM method based on deep reinforcement learning (DRL) is proposed. Experimental data demonstrate that the proposed ViDAR and the VIEO algorithm significantly increase cross-frame co-visibility relationships compared to its corresponding visual-inertial odometry (VIO) algorithm, improving state estimation accuracy. Additionally, the DRL-based active SLAM algorithm, with the ability to decouple from platform motion, can increase the diversity weight of the feature points and further enhance the VIEO algorithm's performance. The proposed methodology sheds fresh insights into both the updated platform design and decoupled approach of active SLAM systems in complex environments.
Open AccessA Novel ViDAR Device With Visual Inertial Encoder Odometry and Reinforcement Learning-Based Active SLAM Method
In the field of multi-sensor fusion for simultaneous localization and mapping (SLAM), monocular cameras and IMUs are widely used to build simple and effective visual-inertial systems. However, limited research has explored the integration of motor-encoder devices to enhance SLAM performance. By incorporating such devices, it is possible to significantly improve active capability and field of view (FOV) with minimal additional cost and structural complexity. This paper proposes a novel visual-inertial-encoder tightly coupled odometry (VIEO) based on a ViDAR (Video Detection and Ranging) device. A ViDAR calibration method is introduced to ensure accurate initialization for VIEO. In addition, a platform motion decoupled active SLAM method based on deep reinforcement learning (DRL) is proposed. Experimental data demonstrate that the proposed ViDAR and the VIEO algorithm significantly increase cross-frame co-visibility relationships compared to its corresponding visual-inertial odometry (VIO) algorithm, improving state estimation accuracy. Additionally, the DRL-based active SLAM algorithm, with the ability to decouple from platform motion, can increase the diversity weight of the feature points and further enhance the VIEO algorithm's performance. The proposed methodology sheds fresh insights into both the updated platform design and decoupled approach of active SLAM systems in complex environments.
- 19 May 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Informatics
- Vol. 21  (8) , 6547-6558
A Novel ViDAR Device With Visual Inertial Encoder Odometry and Reinforcement Learning-Based Active SLAM Method
In the field of multisensor fusion for simultaneous localization and mapping (SLAM), monocular cameras and IMUs are widely used to build simple and effective visual-inertial systems. However, limited research has explored the integration of motor-encoder devices to enhance SLAM performance. By incorporating such devices, it is possible to significantly improve active capability and field of view (FOV) with minimal additional cost and structural complexity. This article proposes a novel visual-inertial-encoder tightly coupled odometry (VIEO) based on a video detection and ranging (ViDAR) device. A ViDAR calibration method is introduced to ensure accurate initialization for VIEO. In addition, a platform motion decoupled active SLAM method based on deep reinforcement learning (DRL) is proposed. Experimental data demonstrate that the proposed ViDAR and the VIEO algorithm significantly increase cross-frame co-visibility relationships compared to its corresponding visual-inertial odometry (VIO) algorithm, improving state estimation accuracy. Additionally, the DRL-based active SLAM algorithm, with the ability to decouple from platform motion, can increase the diversity weight of the feature points and further enhance the VIEO algorithm's performance. The proposed methodology sheds fresh insights into both the updated platform design and decoupled approach of active SLAM systems in complex environments.
- 19 May 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industrial Informatics
- Vol. 21  (8) , 6547-6558
A Novel ViDAR Device With Visual Inertial Encoder Odometry and Reinforcement Learning-Based Active SLAM Method
In the field of multisensor fusion for simultaneous localization and mapping (SLAM), monocular cameras and IMUs are widely used to build simple and effective visual-inertial systems. However, limited research has explored the integration of motor-encoder devices to enhance SLAM performance. By incorporating such devices, it is possible to significantly improve active capability and field of view (FOV) with minimal additional cost and structural complexity. This article proposes a novel visual-inertial-encoder tightly coupled odometry (VIEO) based on a video detection and ranging (ViDAR) device. A ViDAR calibration method is introduced to ensure accurate initialization for VIEO. In addition, a platform motion decoupled active SLAM method based on deep reinforcement learning (DRL) is proposed. Experimental data demonstrate that the proposed ViDAR and the VIEO algorithm significantly increase cross-frame co-visibility relationships compared to its corresponding visual-inertial odometry (VIO) algorithm, improving state estimation accuracy. Additionally, the DRL-based active SLAM algorithm, with the ability to decouple from platform motion, can increase the diversity weight of the feature points and further enhance the VIEO algorithm's performance. The proposed methodology sheds fresh insights into both the updated platform design and decoupled approach of active SLAM systems in complex environments.
- 25 November 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automation Science and Engineering
- Vol. 22  (15455955) , 9218-9229
TFGait—Stable and Efficient Adaptive Gait Planning With Terrain Recognition and Froude Number for Quadruped Robot
Gait planning is one of the most critical technologies for quadruped robots. However, far too little attention has been paid to the tight coupling mechanism of gait planning with terrain understanding and energy efficiency. To date, it is still challenging to plan optimal gait strategies that are highly adapted to terrain features with stable and efficient transitions. Accordingly, this paper proposes an adaptive gait control framework for quadruped robots that combines terrain recognition, Cost of Transport (CoT), and the Froude (Fr) number. More specifically, an optimal gait selection strategy for quadruped robots is designed based on different terrain texture features and the CoT characteristics of different gaits. To address the gait transition process induced thereby, an adaptive method for gait parameters based on the Fr number is further proposed, which can make the process more stable. Besides, model predictive control (MPC) and whole-body control (WBC) are employed as the motion controllers for the quadruped robot. Furthermore, simulation and experimental results indicate that the proposed method possesses superior terrain adaptability, energy efficiency, and motion stability during gait transitions, which is beneficial for the quadruped robots to maintain stable motion and reduce energy consumption when performing tasks in changeable terrains. Note to Practitioners —This paper is motivated by the problem of adaptive gait planning for quadruped robots that walks through different terrains. We propose a method that ensures optimal gait selection by robots facing diverse terrains and maintains the stability of gait transition. The proposed control framework, upon testing in a simulated environment, can be directly deployed on real-world robot without further adjustments and allows the robot to traverse various terrains with minimal sim-to-real issues. Hopefully, our proposed method can provide valuable guidance and support for facilitating the enhancement of capabilities in performing prolonged endurance tasks in unstructured environments for quadruped robots.
- 25 November 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automation Science and Engineering
- Vol. 22  (15455955) , 9218-9229
TFGait—Stable and Efficient Adaptive Gait Planning With Terrain Recognition and Froude Number for Quadruped Robot
Gait planning is one of the most critical technologies for quadruped robots. However, far too little attention has been paid to the tight coupling mechanism of gait planning with terrain understanding and energy efficiency. To date, it is still challenging to plan optimal gait strategies that are highly adapted to terrain features with stable and efficient transitions. Accordingly, this paper proposes an adaptive gait control framework for quadruped robots that combines terrain recognition, Cost of Transport (CoT), and the Froude (Fr) number. More specifically, an optimal gait selection strategy for quadruped robots is designed based on different terrain texture features and the CoT characteristics of different gaits. To address the gait transition process induced thereby, an adaptive method for gait parameters based on the Fr number is further proposed, which can make the process more stable. Besides, model predictive control (MPC) and whole-body control (WBC) are employed as the motion controllers for the quadruped robot. Furthermore, simulation and experimental results indicate that the proposed method possesses superior terrain adaptability, energy efficiency, and motion stability during gait transitions, which is beneficial for the quadruped robots to maintain stable motion and reduce energy consumption when performing tasks in changeable terrains. Note to Practitioners —This paper is motivated by the problem of adaptive gait planning for quadruped robots that walks through different terrains. We propose a method that ensures optimal gait selection by robots facing diverse terrains and maintains the stability of gait transition. The proposed control framework, upon testing in a simulated environment, can be directly deployed on real-world robot without further adjustments and allows the robot to traverse various terrains with minimal sim-to-real issues. Hopefully, our proposed method can provide valuable guidance and support for facilitating the enhancement of capabilities in performing prolonged endurance tasks in unstructured environments for quadruped robots.
- Top Cited Papers
- 5 July 2024
- Published by Springer Nature in Nature Machine Intelligence
- Vol. 6  (7) , 787-798
Lifelike agility and play in quadrupedal robots using reinforcement learning and generative pre-trained models
- 5 July 2024
- Published by Springer Nature in Nature Machine Intelligence
- Vol. 6  (7) , 787-798
Top Cited PapersLifelike agility and play in quadrupedal robots using reinforcement learning and generative pre-trained models
- 28 December 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automation Science and Engineering
- Vol. 21  (4) , 7562-7582
Max: A Wheeled-Legged Quadruped Robot for Multimodal Agile Locomotion
To enrich legged robots with fast energy-efficient mobility on even terrain, wheeled-legged robots have emerged as a valued robot form in robotics research. This paper describes the complete development of a new wheeled-legged quadruped robot named Max, ranging from its mechanical design over system architecture to core algorithms implemented for it to realize various motion behaviors. Instead of attaching wheels to the distal ends of legs as in the existing wheeled-legged robot designs, this robot has wheels installed on the knees with a special switching mechanism to convert a leg between the legged and wheeled locomotion modes. This design keeps the wheeled leg lightweight, enabling the robot to preserve the motion agility as a quadruped robot while gaining the energy-efficiency as a four-wheel or even two-wheel mobile robot. An online locomotion generation method is proposed to compute the 6-D body trajectory of the robot in walking on the perceived terrain, while dynamic movements such as leaps and flips are generated by a unified trajectory optimizer, which is also used to generate the transition motions of the robot to transform into the wheeled mode. The diverse mobility of the proposed robot Max is verified with extensive experiments. Note to Practitioners —Empowering robots with all-terrain mobility is a fundamental open problem in developing a new generation of robots. To this end, combinations of wheels and legs have been explored for robots to possess both traversability on uneven terrains and efficiency on even terrains. This paper proposes a new wheeled-legged quadruped robot with focuses on the integrated design of wheeled legs, system architecture, and core algorithms implemented for various legged and wheeled locomotion behaviors. To embed wheels without adding additional motors and keep the light weight of original legs, a special switching mechanism is designed and integrated at the knee joints where wheels are installed. Algorithms for generating quadrupedal walk according to online perceived terrain information as well as other dynamic legged and wheeled motions are discussed and demonstrated. The system architecture for allocating all vision and motion algorithms is also presented. This work is intended to provide a whole picture of developing this new robot including both hardware and software aspects.
- 28 December 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automation Science and Engineering
- Vol. 21  (4) , 7562-7582
Max: A Wheeled-Legged Quadruped Robot for Multimodal Agile Locomotion
To enrich legged robots with fast energy-efficient mobility on even terrain, wheeled-legged robots have emerged as a valued robot form in robotics research. This paper describes the complete development of a new wheeled-legged quadruped robot named Max, ranging from its mechanical design over system architecture to core algorithms implemented for it to realize various motion behaviors. Instead of attaching wheels to the distal ends of legs as in the existing wheeled-legged robot designs, this robot has wheels installed on the knees with a special switching mechanism to convert a leg between the legged and wheeled locomotion modes. This design keeps the wheeled leg lightweight, enabling the robot to preserve the motion agility as a quadruped robot while gaining the energy-efficiency as a four-wheel or even two-wheel mobile robot. An online locomotion generation method is proposed to compute the 6-D body trajectory of the robot in walking on the perceived terrain, while dynamic movements such as leaps and flips are generated by a unified trajectory optimizer, which is also used to generate the transition motions of the robot to transform into the wheeled mode. The diverse mobility of the proposed robot Max is verified with extensive experiments. Note to Practitioners —Empowering robots with all-terrain mobility is a fundamental open problem in developing a new generation of robots. To this end, combinations of wheels and legs have been explored for robots to possess both traversability on uneven terrains and efficiency on even terrains. This paper proposes a new wheeled-legged quadruped robot with focuses on the integrated design of wheeled legs, system architecture, and core algorithms implemented for various legged and wheeled locomotion behaviors. To embed wheels without adding additional motors and keep the light weight of original legs, a special switching mechanism is designed and integrated at the knee joints where wheels are installed. Algorithms for generating quadrupedal walk according to online perceived terrain information as well as other dynamic legged and wheeled motions are discussed and demonstrated. The system architecture for allocating all vision and motion algorithms is also presented. This work is intended to provide a whole picture of developing this new robot including both hardware and software aspects.
- Open Access
Learning and Reusing Quadruped Robot Movement Skills from Biological Dogs for Higher-Level Tasks
In the field of quadruped robots, the most classic motion control algorithm is based on model prediction control (MPC). However, this method poses challenges as it necessitates the precise construction of the robot’s dynamics model, making it difficult to achieve agile movements similar to those of a biological dog. Due to these limitations, researchers are increasingly turning to model-free learning methods, which significantly reduce the difficulty of modeling and engineering debugging and simultaneously reduce real-time optimization computational burden. Inspired by the growth process of humans and animals, from learning to walk to fluent movements, this article proposes a hierarchical reinforcement learning framework for the motion controller to learn some higher-level tasks. First, some basic motion skills can be learned from motion data captured from a biological dog. Then, with these learned basic motion skills as a foundation, the quadruped robot can focus on learning higher-level tasks without starting from low-level kinematics, which saves redundant training time. By utilizing domain randomization techniques during the training process, the trained policy function can be directly transferred to a physical robot without modification, and the resulting controller can perform more biomimetic movements. By implementing the method proposed in this article, the agility and adaptability of the quadruped robot can be maximally utilized to achieve efficient operations in complex terrains.
Open AccessLearning and Reusing Quadruped Robot Movement Skills from Biological Dogs for Higher-Level Tasks
In the field of quadruped robots, the most classic motion control algorithm is based on model prediction control (MPC). However, this method poses challenges as it necessitates the precise construction of the robot’s dynamics model, making it difficult to achieve agile movements similar to those of a biological dog. Due to these limitations, researchers are increasingly turning to model-free learning methods, which significantly reduce the difficulty of modeling and engineering debugging and simultaneously reduce real-time optimization computational burden. Inspired by the growth process of humans and animals, from learning to walk to fluent movements, this article proposes a hierarchical reinforcement learning framework for the motion controller to learn some higher-level tasks. First, some basic motion skills can be learned from motion data captured from a biological dog. Then, with these learned basic motion skills as a foundation, the quadruped robot can focus on learning higher-level tasks without starting from low-level kinematics, which saves redundant training time. By utilizing domain randomization techniques during the training process, the trained policy function can be directly transferred to a physical robot without modification, and the resulting controller can perform more biomimetic movements. By implementing the method proposed in this article, the agility and adaptability of the quadruped robot can be maximally utilized to achieve efficient operations in complex terrains.
- 12 December 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-8
A Learning Framework for Human-Like Time Parameterization of Robot Manipulation Paths
This paper presents a transformer-based approach to time-parameterize robot manipulation paths in human-centred environments. We propose to build an implicit neural function, named Human Mimic Timing Function (HMTF) to model the spatio-temporal correlations in human motions, which in turn are used to generate human-like and path-consistent temporal features for robot manipulation motions. We train a multi-modal HMTF by imitating human demonstrations and integrate it into a sampling-based pipeline for human-like robot motion planning. Experimental results show that through training on large-scale human demonstrations, our HMTF allows generalization to different manipulation modalities, and can generate smooth and human-like temporal features for random robot paths. Compared with time-optimal path parameterization (TOPP), HMTF is more versatile and achieves significant improvement in the temporal human-likeness when applied to parameterize robot manipulation paths.
- 12 December 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-8
A Learning Framework for Human-Like Time Parameterization of Robot Manipulation Paths
This paper presents a transformer-based approach to time-parameterize robot manipulation paths in human-centred environments. We propose to build an implicit neural function, named Human Mimic Timing Function (HMTF) to model the spatio-temporal correlations in human motions, which in turn are used to generate human-like and path-consistent temporal features for robot manipulation motions. We train a multi-modal HMTF by imitating human demonstrations and integrate it into a sampling-based pipeline for human-like robot motion planning. Experimental results show that through training on large-scale human demonstrations, our HMTF allows generalization to different manipulation modalities, and can generate smooth and human-like temporal features for random robot paths. Compared with time-optimal path parameterization (TOPP), HMTF is more versatile and achieves significant improvement in the temporal human-likeness when applied to parameterize robot manipulation paths.
- 18 July 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Intelligent Vehicles
- Vol. 9  (1) , 670-680
A Collision-Free Target Tracking Controller With Uncertain Disturbance Rejection for Quadruped Robots
With respect to the dynamic target tracking issue in the obstacle environment, this paper provides a collision-free tracking framework combining a modified guidance vector field (GVF) and a disturbance rejection controller. More specifically, two primary improvements are implemented compared with the existing GVF methods. The first improvement involves designing a variable property vector deforming the elliptic integral curves to straight lines pointing to the target point, which prevents the robot from detouring. The other improvement is to construct an adjustable parametric function for blending the attractive field and repulsive field so as to refine the obstacle avoidance performance. Meanwhile, a generalized proportional integral observer (GPIO) based steering controller and a sliding mode based approaching controller are provided to enhance the capability of disturbance rejection. Furthermore, simulation and experimental results demonstrate that the proposed method is efficient in the multi-obstacle environment in terms of tracking the virtual dynamic target and the dynamic quadruped robot target even in the environment with uncertain disturbances.
- 18 July 2023
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Intelligent Vehicles
- Vol. 9  (1) , 670-680
A Collision-Free Target Tracking Controller With Uncertain Disturbance Rejection for Quadruped Robots
With respect to the dynamic target tracking issue in the obstacle environment, this paper provides a collision-free tracking framework combining a modified guidance vector field (GVF) and a disturbance rejection controller. More specifically, two primary improvements are implemented compared with the existing GVF methods. The first improvement involves designing a variable property vector deforming the elliptic integral curves to straight lines pointing to the target point, which prevents the robot from detouring. The other improvement is to construct an adjustable parametric function for blending the attractive field and repulsive field so as to refine the obstacle avoidance performance. Meanwhile, a generalized proportional integral observer (GPIO) based steering controller and a sliding mode based approaching controller are provided to enhance the capability of disturbance rejection. Furthermore, simulation and experimental results demonstrate that the proposed method is efficient in the multi-obstacle environment in terms of tracking the virtual dynamic target and the dynamic quadruped robot target even in the environment with uncertain disturbances.
- 14 April 2021
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Intelligent Transportation Systems
- Vol. 23  (7) , 7457-7468
Unsupervised Occlusion-Aware Stereo Matching With Directed Disparity Smoothing
When handling occlusion in unsupervised stereo matching, existing methods tend to neglect the supportive role of occlusion and to perform inappropriate disparity smoothing around the occlusion. To address these problems, we propose an occlusion-aware stereo network that contains a specific module to first estimate occlusion as an additional depth cue. In the occlusion inference module, a pixel is classified with a three-category label based on whether an area is occluded by an object on the left, occluded by an object on the right, or unoccluded. After the occluders are detected, we introduce a directed disparity smoothing loss that allows valid disparity estimates to be propagated to fill the occluded region, while ambiguous matches in the occluded region do not affect other regions. Disparity and occlusion are trained alternately in an unsupervised manner with detached backpropagation to enable the directed smoothness. Experiments show that our method achieves 3-pixel threshold error rates of 6.51% and 5.69% on the KITTI 2015 and KITTI 2012 validation sets, state-of-the-art results among unsupervised learning networks at the time of submission.
- 14 April 2021
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Intelligent Transportation Systems
- Vol. 23  (7) , 7457-7468
Unsupervised Occlusion-Aware Stereo Matching With Directed Disparity Smoothing
When handling occlusion in unsupervised stereo matching, existing methods tend to neglect the supportive role of occlusion and to perform inappropriate disparity smoothing around the occlusion. To address these problems, we propose an occlusion-aware stereo network that contains a specific module to first estimate occlusion as an additional depth cue. In the occlusion inference module, a pixel is classified with a three-category label based on whether an area is occluded by an object on the left, occluded by an object on the right, or unoccluded. After the occluders are detected, we introduce a directed disparity smoothing loss that allows valid disparity estimates to be propagated to fill the occluded region, while ambiguous matches in the occluded region do not affect other regions. Disparity and occlusion are trained alternately in an unsupervised manner with detached backpropagation to enable the directed smoothness. Experiments show that our method achieves 3-pixel threshold error rates of 6.51% and 5.69% on the KITTI 2015 and KITTI 2012 validation sets, state-of-the-art results among unsupervised learning networks at the time of submission.