Nonholonomic virtual constraints and gait optimization for robust walking control

Abstract

A key challenge in robotic bipedal locomotion is the design of feedback controllers that function well in the presence of uncertainty, in both the robot and its environment. This paper addresses the design of feedback controllers and periodic gaits that function well in the presence of modest terrain variation, without over-reliance on perception and a priori knowledge of the environment. Model-based design methods are introduced and subsequently validated in simulation and experiment on MARLO, an underactuated three-dimensional bipedal robot that is of roughly human size and is equipped with an inertial measurement unit and joint encoders. Innovations include an optimization method that accounts for multiple types of disturbances and a feedback control design that enables continuous velocity-based posture regulation via nonholonomic virtual constraints. Using a single continuously defined controller taken directly from optimization, MARLO traverses sloped sidewalks and parking lots, terrain covered with randomly thrown boards, and grass fields, all while maintaining average walking speeds between 0.9 and 0.98 m/s and setting a new precedent for walking efficiency in realistic environments.

Feedback Control of a Cassie Bipedal Robot: Walking, Standing, and Riding a Segway

“…The desired evolution of the virtual constraints is defined by h d in the output equation (12). This function is constructed using linear interpolation of a discrete library of gaits, each encoding a particular forward walking speed.…”

A Phase Variable Approach for Improved Rhythmic and Non-Rhythmic Control of a Powered Knee-Ankle Prosthesis

“…Originally, virtual constraints were introduced as relationships among generalized positions (angles), which is analogous to a holonomic set of kinematic constraints. More recently, nonholonomic virtual constraints have also been used in legged robots applications [34], [35]. Generally, virtual constraints define the desired trajectories for the controlled degrees of freedom in the following form:…”

An essential model for generating walking motions for humanoid robots

“…On the other hand, a walking gait can be an "automatic" task if the floor is flat and empty, or a task precisely defined by the environment. In the first case, the assumption that the motion of the robot depends only on its internal states is made [7,8,9,10,11]. In the second case, the modeling must be based on a reference linked to the environment to impose a precise pose of the landing foot even in presence of perturbations.…”

“…This model has been developed by taking into account the notion of zero dynamics, which is a very useful tool to analyze the internal dynamics of a system [15]. Among many applications, this tool has also been used to develop walking motions of underactuated systems such as in [16], [9], [11], [17], among others. However, unlike previous works, the original idea in this paper is to define a 3D dynamic relation between the two internal states (usually the horizontal position of the CoM) and the ZMP without the assumptions of the well-known LIP model.…”