Normalized Neural Network for Energy Efficient Bipedal Walking Using Nonlinear Inverted Pendulum Model

In this paper, we present a novel approach for bipedal walking pattern generation. The proposed method is designed based on 2D inverted pendulum model. All control variables are optimized for an energy efficient gait. To obviate the need of solving non-linear dynamics on-line, a deep neural network is adopted for fast non-linear mapping from desired states to control variables. Normalized dimensionless data is generated to train the neural network, therefore, the trained neural network can be applied to bipedal robots of any size, without any specific modification. The proposed method is later verified through numerical simulations. Simulation results demonstrated that the proposed approach can generate feasible walking motions, and regulate robot’s walking velocity successfully. Its disturbance rejection capability was also validated

Globally stable control of a dynamic bipedal walker using adaptive frequency oscillators

We present a control method for a simple limit-cycle bipedal walker that uses adaptive frequency oscillators (AFOs) to generate stable gaits. Existence of stable limit cycles is demonstrated with an inverted-pendulum model. This model predicts a proportional relationship between hip torque amplitude and stride frequency. The closed-loop walking control incorporates adaptive Fourier analysis to generate a uniform oscillator phase. Gait solutions (fixed points) are predicted via linearization of the walker model, and employed as initial conditions to generate exact solutions via simulation. Global stability is determined via a recursive algorithm that generates the approximate basin of attraction of a fixed point. We also present an initial study on the implementation of AFO-based control on a bipedal walker with realistic mass distribution and articulated knee joint

Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability

This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines. One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd

Optimal Reduced-order Modeling of Bipedal Locomotion

State-of-the-art approaches to legged locomotion are widely dependent on the use of models like the linear inverted pendulum (LIP) and the spring-loaded inverted pendulum (SLIP), popular because their simplicity enables a wide array of tools for planning, control, and analysis. However, they inevitably limit the ability to execute complex tasks or agile maneuvers. In this work, we aim to automatically synthesize models that remain low-dimensional but retain the capabilities of the high-dimensional system. For example, if one were to restore a small degree of complexity to LIP, SLIP, or a similar model, our approach discovers the form of that additional complexity which optimizes performance. In this paper, we define a class of reduced-order models and provide an algorithm for optimization within this class. To demonstrate our method, we optimize models for walking at a range of speeds and ground inclines, for both a five-link model and the Cassie bipedal robot.Comment: Submitted to ICRA 202

Variability of Gait is Dependent on Direction of Progression: Implications for Active Control

Typical healthy walking displays greater variability in the mediolateral direction compared to the anteroposterior direction. This greater variability is thought to represent increased uncertainty in movement. As a result, it has been postulated that the mediolateral direction of gait requires more active control by the central nervous system while the anteroposterior direction is controlled through passive actions. However, this theory has only been tested on gait where progression occurs in the anteroposterior direction. Therefore, the purpose of this study was to investigate how the amount of variability is affected if progression occurs in the mediolateral direction using a lateral stepping gait. Results showed the anteroposterior direction had a significantly greater amount of variability than the mediolateral direction (p\u3c0.001). The results do not support current models of a partition of active control to different anatomical planes. Rather, it seems that other physical entities involved in motion, such as momentum and inertia, are able to decrease the dependence on active control from the central nervous system. In a lateral stepping gait, such physical entities were no longer assisting in the anteroposterior direction but had a larger impact in the mediolateral direction as it was the direction of progression. As a result variability in the anteroposterior direction increased. Thus, it is possible to infer increased reliance on active control from the central nervous system in the direction orthogonal to progression

Shimyureta to jikki o mochiita haiburiddo-gata kikai gakushuho ni kansuru kenkyu

制度:新 ; 報告番号:甲2816号 ; 学位の種類:博士(工学) ; 授与年月日:2009/2/25 ; 早大学位記番号:新503

Motion Planning and Control for the Locomotion of Humanoid Robot

This thesis aims to contribute on the motion planning and control problem of the locomotion of humanoid robots. For the motion planning, various methods were proposed in different levels of model dependence. First, a model free approach was proposed which utilizes linear regression to estimate the relationship between foot placement and moving velocity. The data-based feature makes it quite robust to handle modeling error and external disturbance. As a generic control philosophy, it can be applied to various robots with different gaits. To reduce the risk of collecting experimental data of model-free method, based on the simplified linear inverted pendulum model, the classic planning method of model predictive control was explored to optimize CoM trajectory with predefined foot placements or optimize them two together with respect to the ZMP constraint. Along with elaborately designed re-planning algorithm and sparse discretization of trajectories, it is fast enough to run in real time and robust enough to resist external disturbance. Thereafter, nonlinear models are utilized for motion planning by performing forward simulation iteratively following the multiple shooting method. A walking pattern is predefined to fix most of the degrees of the robot, and only one decision variable, foot placement, is left in one motion plane and therefore able to be solved in milliseconds which is sufficient to run in real time. In order to track the planned trajectories and prevent the robot from falling over, diverse control strategies were proposed according to the types of joint actuators. CoM stabilizer was designed for the robots with position-controlled joints while quasi-static Cartesian impedance control and optimization-based full body torque control were implemented for the robots with torque-controlled joints. Various scenarios were set up to demonstrate the feasibility and robustness of the proposed approaches, like walking on uneven terrain, walking with narrow feet or straight leg, push recovery and so on