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Asynchronous Real-Time Optimization of Footstep Placement and Timing in Bipedal Walking Robots

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Document pages: 8 pages

Abstract: Online footstep planning is essential for bipedal walking robots to be ableto walk in the presence of disturbances. Until recently this has been achievedby only optimizing the placement of the footstep, keeping the duration of thestep constant. In this paper we introduce a footstep planner capable ofoptimizing footstep placement and timing in real-time by asynchronouslycombining two optimizers, which we refer to as asynchronous real-timeoptimization (ARTO). The first optimizer which runs at approximately 25 Hz,utilizes a fourth-order Runge-Kutta (RK4) method to accurately approximate thedynamics of the linear inverted pendulum (LIP) model for bipedal walking, thenuses non-linear optimization to find optimal footsteps and duration at a lowerfrequency. The second optimizer that runs at approximately 250 Hz, usesanalytical gradients derived from the full dynamics of the LIP model andconstraint penalty terms to perform gradient descent, which finds approximatelyoptimal footstep placement and timing at a higher frequency. By combining thetwo optimizers asynchronously, ARTO has the benefits of fast reactions todisturbances from the gradient descent optimizer, accurate solutions that avoidlocal optima from the RK4 optimizer, and increases the probability that afeasible solution will be found from the two optimizers. Experimentally, weshow that ARTO is able to recover from considerably larger pushes and producesfeasible solutions to larger reference velocity changes than a standardfootstep location optimizer, and outperforms using just the RK4 optimizeralone.

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