Socially Acceptable Bipedal Robot Navigation via Social Zonotope Network Model Predictive Control

TL;DR

The Social Zonotope Network (SZN) is proposed, a novel neural network that couples pedestrian future trajectory prediction and robot motion planning to facilitate socially aware navigation for bipedal robots such as Digit, designed by Agility Robotics.

Abstract

This study addresses the challenge of social bipedal navigation in a dynamic, human-crowded environment, a research area largely underexplored in legged robot navigation. We present a zonotope-based framework that couples prediction and motion planning for a bipedal ego-agent to account for bidirectional influence with the surrounding pedestrians. This framework incorporates a Social Zonotope Network (SZN), a neural network that predicts future pedestrian reachable sets and plans future socially acceptable reachable set for the ego-agent. SZN generates the reachable sets as zonotopes for efficient reachability-based planning, collision checking, and online uncertainty parameterization. Locomotion-specific losses are added to the SZN training process to adhere to the dynamic limits of the bipedal robot that are not explicitly present in the human crowds data set. These loss functions enable the SZN to generate locomotion paths that are more dynamically feasible for improved tracking. SZN is integrated with a Model Predictive Controller (SZN-MPC) for footstep planning for our bipedal robot Digit. SZN-MPC solves for collision-free trajectory by optimizing through SZN's gradients. and Our results demonstrate the framework's effectiveness in producing a socially acceptable path, with consistent locomotion velocity, and optimality. The SZN-MPC framework is validated with extensive simulations and hardware experiments.

Figures (19)

• Figure 1: (top) Snapshot of the proposed social path planner demonstrated on hardware with $5$ pedestrians with pedestrian's prediction zonotopes (green), ego-agent's social zonotope (cyan), and goal location (yellow star) superimposed. (bottom) shows a top-down view of the ego-agent's path, pedestrians' prediction, and social zonotopes.
• Figure 2: Block diagram of the proposed framework. The framework is developed around the Social Zonotope Network (SZN) (Sec. \ref{['sec:social_zono_net']}), which is composed of two sub-networks: the Pedestrian Prediction Network (PPN) and the Ego-agent Social Network (ESN) shown in green and cyan, respectively. Given an environment with observed pedestrians and a goal location, the social path planner designs a social path for Digit (Sec. \ref{['subsec:cost']}). At the middle level, SZN-MPC optimizes through SZN to generate both collision-free and socially acceptable trajectories for Digit (Sec. \ref{['sec:SDMPC']}). The optimal trajectory is then sent to the ALIP controller Gong2022AngularMomentum to generate the desired foot placement for reduced-order optimal trajectory tracking. An ankle-actuated-passivity-based controller sadeghian2017passivityshamsah2023integrated is implemented on Digit for full-body trajectory tracking. Digit current velocity and the optimal trajectory from SZN-MPC are used in the modeling error GP to compensate for the modeling uncertainty between ROM dynamics and full-order dynamics (Sec. \ref{['subsec:Modelling_error_refinements']}).
• Figure 3: Comparison between two different designs of socially acceptable paths. (a) shows a minimally invasive path design for the robot as in moder2022proactiveschaefer2021leveraging, i.e., the robot adjusts its path to not alter the pedestrian's original path or change it in a minimally-invasive way. (b) shows the bidirectionally influenced path between the robot and the pedestrian that our work employs, i.e., the robot and the pedestrian mutually react to each other and adjust their own paths accordingly.
• Figure 4: Illustration of the Linear Inverted Pendulum model for two consecutive foot contact switching states $\boldsymbol{x} _{q}$ and $\boldsymbol{x} _{q+1}$. The shaded yellow regions indicate the kinematics constraint on the control input $\boldsymbol{u}$ detailed in Sec. \ref{['subsec:kin_const']}.
• Figure 5: An illustration of zonotopes: (a) a 3-D zontope ($n=3$) with $n_G=13$ (b) a 2-D zonotope ($n=2$) with $n_G=3$. Red arrows indicate the generators in $G$, with only 6 out of 13 generators are illustrated in (a). In this study, we will use the 2-D zonotopes for our reachability path design.

Theorems & Definitions (13)

• Definition 3.1: Locomotion safety
• Definition 3.2: Navigation safety
• Definition 3.3: Socially acceptable path for bipedal systems
• Proposition 4.2
• Proposition 4.3
• Definition 4.1: Social Zonotope $\mathcal{Z} ^{\rm ego} _{q}$
• Remark 1
• Remark 2
• Remark 3
• Remark 4