No abstract

For bipedal robots to walk over complex and constrained environments (e.g., narrow walkways, stepping stones), they have to meet precise control objectives of speed and foot placement at every single step. This control that achieves the objectives precisely at every step is known as one-step deadbeat control. The high dimensionality of bipedal systems and the under-actuation (number of joint exceeds the actuators) presents a formidable computational challenge to achieve real-time control. In this paper, we present a computationally efficient method for one-step deadbeat control and demonstrate it on a 5-link planar bipedal model with 1 degree of under-actuation. Our method uses computed torque control using the 4 actuated degrees of freedom to decouple and reduce the dimensionality of the stance phase dynamics to a single degree of freedom. This simplification ensures that the step-to-step dynamics are a single equation. Then using Monte Carlo sampling, we generate data for approximating the step-to-step dynamics followed by curve fitting using a control affine model and a Gaussian process error model. We use the control affine model to compute control inputs using feedback linearization and fine tune these using iterative learning control using the Gaussian process error enabling one-step deadbeat control. We demonstrate the approach in simulation in scenarios involving stabilization against perturbations, following a changing velocity reference, and precise foot placement. We conclude that computed torque control-based model reduction and sampling-based approximation of the step-to-step dynamics provides a computationally efficient approach for real-time one-step deadbeat control of complex bipedal systems.

To walk over constrained environments, bipedal robots must meet concise control objectives of speed and foot placement. The decisions made at the current step need to factor in their effects over a time horizon. Such step-to-step control is formulated as a two-point boundary value problem (2-BVP). As the dimensionality of the biped increases, it becomes increasingly difficult to solve this 2-BVP in real-time. The common method to use a simple linearized model for real-time planning followed by mapping on the high dimensional model cannot capture the nonlinearities and leads to potentially poor performance for fast walking speeds. In this paper, we present a framework for real-time control based on using partial feedback linearization (PFL) for model reduction, followed by a data-driven approach to find a quadratic polynomial model for the 2-BVP. This simple step-to-step model along with constraints is then used to formulate and solve a quadratically constrained quadratic program to generate real-time control commands. We demonstrate the efficacy of the approach in simulation on a 5-link biped following a reference velocity profile and on a terrain with ditches. A video is here: https://youtu.be/-UL-wkv4XF8.

For artificial legs that are used in legged robots, exoskeletons, and prostheses, it suffices to achieve velocity regulation at a few key instants of swing rather than tight trajectory tracking. Here, we advertise an event-based, intermittent, discrete controller to enable set-point regulation for problems that are traditionally posed as trajectory following. We measure the system state at prior-chosen instants known as events (e.g., vertically downward position), and we turn on the controller intermittently based on the regulation errors at the set point. The controller is truly discrete, as these measurements and controls occur at the time scale of the system to be controlled. To enable set-point regulation in the presence of uncertainty, we use the errors to tune the model parameters. We demonstrate the method in the velocity control of an artificial leg, a simple pendulum, with up to 50% mass uncertainty. Starting with a 100% regulation error, we achieve velocity regulation of up to 10% in about five swings with only one measurement per swing.