In this letter, we propose a locomotion training framework where a control policy and a state estimator are trained concurrently. The framework consists of a policy network which outputs the desired joint positions and a state estimation network which outputs estimates of the robot’s states such as the base linear velocity, foot height, and contact probability. We exploit a fast simulation environment to train the networks and the trained networks are transferred to the real robot. The trained policy and state estimator are capable of traversing diverse terrains such as a hill, slippery plate, and bumpy road. We also demonstrate that the learned policy can run at up to 3.75 m/s on normal flat ground and 3.54 m/s on a slippery plate with the coefficient of friction of 0.22.

Concurrent Training of a Control Policy and a State Estimator for Dynamic and Robust Legged Locomotion

Actuating systems for the proprioceptive control of legged robots must have a high mechanical efficiency and mechanical bandwidth for high torque transmission to avoid power transmission losses. We developed a high-efficiency compact cycloidal reducer for legged robots that uses needle roller bearings in all parts where contact occurs during the power transfer process inside the reducer, which greatly improves the efficiency compared to a cycloidal reducer using free rollers. We also proposed a subcarrier structure that distributes the load and allows the cycloidal reducer to respond robustly to impacts that may occur during the locomotion of the legged robot. The subcarrier increases the stiffness, which improves the mechanical bandwidth. A cycloidal reducer was manufactured with > 90% efficiency in most operating ranges; it weighs 766 g and can withstand a torque of more than 155 Nm. The cycloidal reducer module coupled with the motor indicated a torque control bandwidth of 72 Hz, so it can be used for legged robots with agile motions.

Development of a Lightweight and High-efficiency Compact Cycloidal Reducer for Legged Robots

This letter presents a state estimation algorithm for the legged robot by defining the problem as a Maximum A Posteriori (MAP) estimation problem and solving the problem with the Gauss-Newton algorithm. Moreover, marginalization by the Schur Complement method is adopted to make a fixed size problem. Each component of the cost function and its Jacobian are derived utilizing the SO(3) manifold structure, while we reparameterize the state with nominal state and variation to make linear algebra and vector calculus applied properly. Furthermore, a slip rejection method is proposed to reduce the erroneous effect of fault modeling of kinematics models. The proposed algorithm is verified by comparison with the Invariant Extended Kalman Filter (IEKF) in real robot experiments on various environments.

Legged Robot State Estimation With Dynamic Contact Event Information

An improved active disturbance rejection control (I-ADRC) to improve the disturbance attenuation of a permanent magnet synchronous motor speed controller was proposed in this paper. A nonlinear function with improved smoothness was adopted to design the controller. The Lyapunov stability of the improved tracking differentiator, the improved extended state observer, and the controller were analysed. Moreover, simulations and experiments confirmed the effectiveness of the proposed controller. The results demonstrate that the proposed controller has a smaller steady-state error and a stronger disturbance attenuation ability than the proportional integral derivative (PID) controller.

https://www.mdpi.com/2076-0825/10/7/147/pdf

Permanent Magnet Synchronous Motor Speed Control Based on Improved Active Disturbance Rejection Control

Machining robots are expected to significantly change existing production systems in the near future. The quality of the machining process with robots is mainly governed by the accuracy and stiffness of the robots. Therefore, a precision reducer for the robot joint is an important component that governs the accuracy of machining robots. This paper presents a review of rigid precision reducers for machining robots. Initially, an overview of the machining robots and their features is introduced. The importance of a precision reducer as a component of a robot for machining is explored. A cycloid reducer is the best candidate among precision reducers, considering both the structural compliance and kinematic accuracy of the machining robots. This is followed by reviews of various cycloid reducers and their operating principles. The design issues of the cycloid reducer for performance improvement are then presented. Additionally, the methodology and analysis to assess the performance of the cycloid reducers are discussed. The machining and fault detection of a cycloid reducer are briefly addressed. Finally, other applications of cycloid reducers are introduced.

https://link.springer.com/content/pdf/10.1007/s12541-021-00552-8.pdf

Rigid Precision Reducers for Machining Industrial Robots

This paper presents a constrained nonlinear model predictive control (NMPC) framework for legged locomotion. The framework assumes a legged robot as a floating base single rigid body with contact forces being applied to the body as external forces. With consideration of orientation dynamics evolving on the rotation manifold SO(3), analytic Jacobians which are necessary for constructing the gradient and the Gauss-Newton Hessian approximation of the objective function are derived. This procedure also includes the reparameterization of the robot orientation on SO(3) to orientation error in the tangent space of that manifold. Obtained gradient and Gauss-Newton Hessian approximation are utilized to solve nonlinear least squares problems formulated from NMPC in a computationally efficient manner. The proposed algorithm is verified on various types of legged robots and gaits in a simulation environment.

Real-Time Constrained Nonlinear Model Predictive Control on SO(3) for Dynamic Legged Locomotion*

Most state-of-the-art torque control-based legged robots show excellent performance, exceeding that of conventional position control-based robots. Many conventional position control-based legged robots have high gear ratios, but do not have joint torque sensors. In addition, some robots cannot generate current for controlling the motor torque. To apply torque control-based walking algorithms to a position control-based humanoid robot, we proposed current control using a motor thermal model and realized joint torque control by compensating for the joint dynamics and robot dynamics. We conducted experiments to verify the performance of the Hubo2 platform developed in 2008 by applying a full-body dynamics control framework. The results confirmed the possibility of using torque control algorithms with existing position-based robots.

Seungwoo Hong

Papers

Real-Time Constrained Nonlinear Model Predictive Control on SO(3) for Dynamic Legged Locomotion*

Development of a Lightweight and High-efficiency Compact Cycloidal Reducer for Legged Robots

Legged Robot State Estimation With Dynamic Contact Event Information

Implementing Full-body Torque Control in Humanoid Robot with High Gear Ratio Using Pulse Width Modulation Voltage

Finite element methods for the Stokes problem in R3