<p>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 (2BVP).&nbsp;As the dimensionality of the biped increases, it becomes increasingly difficult to solve this 2-two-point boundary value problem (2BVP)&nbsp;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 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 constraint 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. Future work will explore hardware implementation of the approach.&nbsp;A short video is here posted on this link: https://youtu.be/-UL-wkv4XF8</p>

Optimal Control of a 5-Link Biped Using Quadratic Polynomial Model of Two-Point Boundary Value Problem

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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