Learning-Based Control

Barrier-Based Style Rewards

A Learning Framework for Diverse Legged Robot Locomotion
Using Barrier-Based Style Rewards [ICRA'25] :
Introduces a reinforcement learning framework for legged robot locomotion that supports multiple motion modes, such as quadruped, tripod, and biped, on a single robot platform. To address the challenge of achieving natural and versatile motion without relying on predefined trajectories or heavy reward engineering, the method employs a barrier-based style reward using a relaxed logarithmic function, which guides the motion style such as gait, foot clearance, joint posture, and body height. The proposed framework enables the robot to adapt its motion style to diverse tasks. In quadrupedal mode, the robot can traverse uneven terrain, gallop at 4.67 m/s, and overcome obstacles up to 58 cm (67 cm for HOUND2). In bipedal mode, it is capable of running at 3.6 m/s, carrying a 7.5 kg object, and ascending stairs—all performed without exteroceptive input.

High-Speed Quadrupedal Locomotion

Reinforcement Learning for High-Speed Quadrupedal Locomotion With Motor Operating Region Constraints: Mitigating Motor Model Discrepancies through Torque Clipping in Realistic Motor Operating Region [R-AM'24] :
This paper presents a method for achieving highspeed running of a quadruped robot by considering the actuator torque-speed operating region in reinforcement learning. The physical properties and constraints of the actuator are included in the training process to reduce state transitions that are infeasible in the real world due to motor torque-speed limitations. The gait reward is designed to distribute motor torque evenly across all legs, contributing to more balanced power usage and mitigating performance bottlenecks due to single-motor saturation. With the trained policy, KAIST Hound, a 45 kg quadruped robot, can run up to 6.5 m/s, which is the fastest speed among electric motor-based quadruped robots.

Model-Based Control

Trajectory Optimization

Dynamically-Consistent Trajectory Optimization for Legged Robots via Contact Point Decomposition [Under Review in RA-L] :
To generate both dynamically feasible motions and contact sequences simultaneously, we propose a Phase-Based Trajectory Optimization (PBTO) framework that leverages dynamics decoupling. In this framework, the translational dynamics at each contact point are formulated as a Multiple-Phase Optimal Control problem, improving overall dynamic consistency. Moreover, by exploiting the properties of Bézier polynomials and employing SO(3) representations, the proposed method enhances feasibility in translational dynamics, friction cone constraints, and angular dynamics compared to previous PBTO approaches.

Contact-implicit Model Predictive Control

Contact-implicit Model Predictive Control: Controlling diverse quadruped motions without pre-planned contact modes or trajectories [IROS'22, IJRR'24] :
This paper presents a contact-implicit MPC framework for discovering multi-contact motions without predefined contact sequences, using a DDP approach combined with linear complementarity constraints. It introduces smooth analytical gradients of contact impulses via relaxed constraints to explore diverse contact modes. The method also incorporates differentiable cost terms to shape foot trajectories and uses a multiple shooting strategy to stabilize the optimization process.

Nonlinear Representation-free Model Predictive Control on SO(3)

Real-Time Constrained Nonlinear Model Predictive Control on SO(3) for Dynamic Legged Locomotion [IROS'20, Best RoboCup Paper] : 
In this work, a novel NMPC framework for dynamic legged locomotion and an efficient algorithm to solve this constrained nonlinear optimization problem are presented. The orientation of the robot among the components that make up the objective function of the optimization problem adopts the manifold configuration of the rotation group.

Linear Model Predictive Control on SO(3)

Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds [lCRA'19, T-RO'21 (TC Best Paper Finalist)] :
This paper deals with our Model Predictive Control framework on the SO(3) manifold. To solve the MPC problem efficiently, linearization at some appropriate operating point and vectorization of the variables are required.

Optimal Motion Generation

Online Optimization for Jumps over Obstacles [RSS'15, RAS'21] :
The main objective of the study is to present a controller design scheme which provides a robust running gait of a quadruped robot with the ability to change the running speed over a wide range while handling variations in ground height and stiffness. 

Sparsity Analysis

Sparse QP Solver for MPC [RA-L'19] :
For solving optimization problem, complex matrix manipulations are necessary. All the matrices we have known are categorized as two group, dense and sparse, according to the proportion of the zero elements in the matrix. Sparse matrix can posses surprisingly high computational saving depending on the algorithm. Our algorithm for sparsity matrix manipulation have very high performance comparing with other state-of-art theories.