Asymptotically Stable Gait Generation and Instantaneous Walkability Determination for Planar Almost Linear Biped with Knees
Fumihiko Asano, NING LEI, Taiki Sedoguchi
AI summary
Problem
Real-time assessment of bipedal robot walkability and stability is hindered by the heavy computational cost of numerical integration and complex hybrid dynamics analysis.
Approach
The authors derive a 3-DOF reduced linearized model by approximating the gravity term around a specific expansion point, then discretize it to allow instantaneous iterative state prediction.
Key results
- Derivation of a 6-DOF nonlinear model and asymptotically stable gait controller for a planar biped with knees
- Development of a reduced 3-DOF linearized model enabling instantaneous future state calculation
- Demonstration of negligible-time walkability determination through iterative discretization
- Quantification of how knee flexion angle and linearization expansion point impact approximation accuracy
Why it matters
Provides a computationally lightweight framework for real-time stability and path feasibility checks in complex terrains for legged robotics.
Abstract
A class of planar bipedal robots with unique mechanical properties has been proposed, where all links are balanced around the hip joint, preventing natural swinging motion due to gravity. A common property of their equations of motion is that the inertia matrix is a constant matrix, there are no nonlinear velocity terms, and the gravity term contains simple nonlinear terms. By performing a Taylor expansion of the gravity term and making a linear approximation, it is easy to derive a linearized model, and calculations for future states or walkability determination can be performed instantaneously without the need for numerical integration. This paper extends the method to a planar biped robot model with knees. First, we derive the equations of motion, constraint conditions, and inelastic collisions for a planar 6-DOF biped robot, design its control system, and numerically generate a stable bipedal gait on a horizontal plane. Next, we reduce the equations of motion to a 3-DOF model, and derive a linearized model by approximating the gravity term as linear around the expansion point for the thigh frame angle. Through numerical simulations, we demonstrate that calculations for future states and walkability determination can be completed in negligible time. By applying control inputs to the obtained model, performing state-space realization, and then discretizing it, instantaneous walkability determination through iterative calculation becomes possible. Through detailed gait analysis, we discuss how the knee joint flexion angle and the expansion point affect the accuracy of the linear approximation, and the issues that arise when descending a small step.