The Boundaries of Walking Stability: Viability and Controllability of Simple Models

Petr Zaytsev, Wouter Wolfslag, Andy Ruina

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

From which states and with what controls can a biped avoid falling or reach a given target state? What is the most robust way to do these? So as to help with the design of walking robot controllers, and perhaps give insights into human walking, we address these questions using two simple 2-D models: the inverted pendulum (IP) and linear inverted pendulum (LIP). Each has one state variable at mid-stance, i.e., hip velocity, and two state-dependent controls at each step, i.e., push-off magnitude and step length (IP) and step time and length (LIP). Using practical targets and constraints, we compute all combinations of initial states and control actions for the next step, such that the robot can, with the best possible future controls, avoid falling for n steps or reach a target within n steps. All such combinations constitute regions in the combined space of states and controls. Farther from the boundaries of these regions, the robot tolerates larger errors and disturbances. Furthermore, for these models, and thus possibly real bipeds, usually if it is possible to avoid falling, it is possible to reach the target, and if it is possible to reach the target, it is possible to do so in two steps.
Index Terms—Controllability, legged locomotion, robot control, robustness, viability.
Original languageEnglish
Pages (from-to)336-352
Number of pages17
JournalIEEE Transactions on Robotics
Issue number2
Early online date12 Feb 2018
Publication statusPublished - 12 Apr 2018


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