Research

(Draft) Contact and gait implicit optimization for legged robots is a significant challenge, vital for a range of tasks and effective adaptation to disturbances. Due to the discrete nature of the problem parts, which inherently cannot be differentiated, searching-based algorithms are essential for discovering new and improved gait sequences. In this paper, we introduce a novel framework that segments the problem, applying Differential Dynamics Programming (DDP) to address the continuous aspects and A*-based searching to address the discrete aspects. Incorporating a relaxed model for the head phases, this framework constructs the contact mode in reverse order, thereby generating a decision tree. This tree is characterized by an approximated lower bound for the cost-to-here and an accurately computed cost-to-go, both resolved through the continuous DDP solver. To identify superior gait sequences, the framework employs a hybrid search algorithm, merging the principles of depth-first and A*-search. Benefiting from the relaxed model, our approach employs the lifting and projection of the control tape between the relaxed and constrained models, thereby enhancing the efficiency of the warm start process. Implemented as a model predictive control (MPC) strategy, our method effectively balances performance with computational speed, requiring only about 20 DDP evaluations per MPC iteration. Our simulations prove that our approach can create suitable walking sequences that respond well to changes in speed and external disruptions.

A fundamental problem in legged locomotion is to verify whether a desired trajectory satisfies all physical constraints, especially those for maintaining contacts. Although foot tipping can be avoided via the Zero Moment Point (ZMP) condition, preventing foot sliding and twisting leads to the more complex Contact Wrench Cone (CWC) constraints. This paper proposes an efficient algo- rithm to certify the inclusion of a net contact wrench in the CWC on flat ground with uniform friction. In addition to checking the ZMP criterion, the proposed method also verifies whether the linear force and the yaw moment are feasible. The key step in the algorithm is a novel exact geometric characterization of the yaw moment limits in the case when the support polygon is approximated by a single supporting line. We propose two approaches to select this approx- imating line, providing an accurate inner approximation of the ground truth yaw moment limits with only 18.80% (resp. 7.13%) error. The methods require only 1/150 (resp. 1/139) computation time compared to the exact CWC based on conic programming. As a benchmark, approximating the CWC using square friction pyramids requires similar computation time as the exact CWC, but has >19.35% error. Unlike the ZMP condition, our method provides a sufficient condition for contact wrench feasibility.

This paper presents a control strategy for quadruped robots to hop on their rear legs in three-dimensional space. The proposed approach generates nominal center of mass (CoM) trajectories based on a template spring-loaded inverted pendulum (SLIP) model. Tracking this reference remains a challenge due to the underactauted nature of balance with point feet. To address this challenge, a control-Lyapunov function based quadratic programming (CLF-QP) controller is pro- posed, which modulates nominal ground reaction forces (GRFs) to balance the torso while considering friction limits. The CLF construction is guided by a variational-based linearization (VBL) applied to a reduced-order single-rigid-body (SRB) model, and treats underactuation via solving a Riccati equation to obtain the CLF. A new balance control approach is presented that effectively decouples sagittal plane control (via re-planning) with lateral and rotational control (via the CLF and VBL). The proposed approach shows more robust balancing performance than the conventional CLF-QP approach. Simulations of the Mini Cheetah demonstrate in-place hopping with up to a 0.71m apex height.

I led the quadruped robot project as my graduation design in Wei Zhang's lab in SUSTech, China. My thesis topic is "Mechatronics Design and Analysis of Quadruped Robots". I will also make effort on the locomotion and gait control based on the deep learning. Till now, I have designed a high torque density actuator (max torque 48N.m but only 107mm*48mm overall size) and hip joint. 

My tutor, Prof. Wei Zhang is a new professor who just came from The Ohio State University, his personal webpage is available here: Prof. Wei Zhang.

In the summer of 2018, my classmate ZHU and I participated in the iSURE, a student exchange program between SUSTech and ND, and came to Professor Patrick's lab in ND to participate in his robotics research project. Professor Patrick has just finished his postdoctoral career at Professor Sangbae Kim (representative results: cheetah robot) in MIT and has come to ND to continue research on robotics control, especially quadruped robots. When we arrived, Professor Patrick had just a Jumping Leg Robot for simple testing and learning but there were a lot of bugs that haven't been solved. He hoped that we could help him solve some problems on the hardware platform through this robot. We first abandoned the original buggy and messy Matlab simulation platform, built a new physical simulation environment on Webots, and rewrote many of the underlying controllers. Finally, due to the time relationship we were unable to use the advanced control methods that Patrick recommended, otherwise, we proposed our own control methods and got quite good results.

In my third year at university, I got into Prof. Chenglong Fu's Humanoid Robot and Exoskeleton Lab, as a student assistant. The main projects I have been participate in are the Active Prosthetic and the Passive Flexible Exoskeleton. The first one was the continuation of Prof. Fu's robotic thigh prosthetic project in Tsinghua, and the project on laser radar environment perception during my summer vacation was a branch of this prosthetic project. After entering Prof. Fu's lab, I made some minor contributions to the prosthetic project. 

At the beginning of 2018, I began to expect to start my own research project. I just thought that Professor Fu’s original topic of a passive exoskeleton in Tsinghua inspired me. I began to think that if we transfer the joints energy from left leg to right and from right to left, can we simplify the mechanism of the passive exoskeleton which is the key part in controlling the release timing of the energy storage device. My classmate Zeyu Lu is also very interested in this. As a result, the second project Passive Flexible Exoskeleton was officially launched. At present, the subject is in the stage of experimental analysis, and I will continue to complete this part.

After the sophomore year, I participated in the laboratory exchange study project of the department of MEE, and came to the robot laboratory of Professor Chenglong Fu at Tsinghua University in Beijing. Professor Fu's research interests are humanoid robots, exoskeletons, and prostheses. He gave us the topic of assisting his robotic thigh prosthesis: using lidar (aka. laser radar) for environmental perception and feedback the results to the prosthesis to guide the movement of the prosthesis and the intentional identification of the wearer. We first designed a housing for the lidar to mount the IMU and wear it on the waist. In this way, we can obtain the obstacles and pavement information on the sagittal plane of the prosthesis, and the movement of the waist during human walking is not large, which is convenient for us to stabilize the radar map electronically through the IMU. I wrote a multi-threaded platform for radar to receive data and analyze it (on Python 3.6), and then tested the performance of multiple recognition algorithms with the help of senior in Tsinghua. Finally, we got remarkable recognition results.