# Walking Pattern Generation Through Step-by-Step Quadratic Programming for Biped Robots

## TL;DR

This paper introduces a new method for generating stable walking patterns for biped robots using quadratic programming to optimize motion.

## Contribution

The novel integration of double and single support phases into a unified step for trajectory generation using quadratic optimization.

## Key findings

- The proposed method shortens the optimization horizon while generating natural walking trajectories.
- Vertical COM adjustments are enabled without losing linearity in the optimization problem.
- Simulations and experiments on Neubot validate the method's effectiveness on flat ground and stairs.

## Abstract

The control of a biped robot is a challenging task due to the hard-to-stabilize dynamics. Generating a suitable walking reference trajectory is a key aspect of this problem. This article proposes a novel method of generating walking patterns for biped robots. The method integrates the double support phase and the single support phase into one step, and uses this step as the unit for trajectory generation through quadratic optimization with terminal constraints based on the Linear Inverted Pendulum Model, enabling us to shorten the optimization horizon while still generating natural walking trajectories. Moreover, by restricting the position and acceleration of the center of mass (COM) in the vertical direction, an excessive constraint is formed on the Zero Moment Point (ZMP) to offset the nonlinear effects of the COM’s vertical motion on the ZMP. This allows the COM of the robot to change in the vertical direction while maintaining the linearity of the optimization problem. Finally, the performance of the proposed method is validated by simulations and experiments of walking on flat ground and stairs using a position-controlled biped robot, Neubot.