Simultaneous Ground Reaction Force and State Estimation via Constrained Moving Horizon Estimation

Abstract

Accurate ground reaction force (GRF) estimation can significantly improve the adaptability of legged robots in various real-world applications. For instance, with estimated GRF and contact kinematics, the locomotion control and planning assist the robot in overcoming uncertain terrains. The canonical momentum-based methods, formulated as nonlinear observers, do not fully address the noisy measurements and the dependence between floating-base states and the generalized momentum dynamics. In this paper, we present a simultaneous ground reaction force and state estimation framework for legged robots, which systematically addresses the sensor noise and the coupling between states and dynamics. With the floating base orientation estimated separately, a decentralized Moving Horizon Estimation (MHE) method is implemented to fuse the robot dynamics, proprioceptive sensors, exteroceptive sensors, and deterministic contact complementarity constraints in a convex windowed optimization. The proposed method is shown to be capable of providing accurate GRF and state estimation on several legged robots, including the custom-designed humanoid robot Bucky, the open-source educational planar bipedal robot STRIDE, and the quadrupedal robot Unitree Go1, with a frequency of 200Hz and a past time window of 0.04s.

Figures (7)

• Figure 1: Illustration of the proposed decentralized estimation framework for estimation on various legged robots, including the humanoid robot Bucky (left) and the quadrupedal robot B1 (right). The experiment video is available at: https://youtu.be/Bih7cslSkTo.
• Figure 2: Sensor configurations of (a) Bucky and (b) STRIDE. (c) Sensor configuration and experimental setup of the Unitree Go1.
• Figure 3: The proposed decentralized estimation framework with its application to the quadrupedal robot Go1.
• Figure 4: Estimation results on STRIDE in simulation: $f_z$ and $f_x$ denote the vertical normal force and the tangential frictional force, respectively.
• Figure 5: Estimation results of the GRF on Bucky in simulation, $f_x$, $f_y$, and $f_z$ denote the tangential frictional force and the vertical normal force, respectively, expressed in the world frame.