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Learning Neural Observer-Predictor Models for Limb-level Sampling-based Locomotion Planning

Abhijeet M. Kulkarni, Ioannis Poulakakis, Guoquan Huang

TL;DR

The paper tackles safe, limb-aware locomotion planning by learning a full-body motion predictor anchored by a provably stable neural observer. A decoupled observer-predictor architecture recovers latent states from history and offers a fast GRU-based predictor capable of parallel trajectory rollouts, enabling real-time MPPI planning with limb-level collision checks. The authors introduce joint end-to-end training with a contraction-based stability term, build robust robocentric datasets from simulation and real hardware, and demonstrate significant improvements in goal-pose tracking and collision avoidance on the Vision60 quadruped. Hardware experiments show real-time planning at 25 Hz with thousands of trajectory evaluations, outperforming a traditional kinematic baseline in cluttered environments. The approach provides a scalable, safety-guaranteed foundation for high-performance, collision-aware planning in dynamic legged robots.

Abstract

Accurate full-body motion prediction is essential for the safe, autonomous navigation of legged robots, enabling critical capabilities like limb-level collision checking in cluttered environments. Simplified kinematic models often fail to capture the complex, closed-loop dynamics of the robot and its low-level controller, limiting their predictions to simple planar motion. To address this, we present a learning-based observer-predictor framework that accurately predicts this motion. Our method features a neural observer with provable UUB guarantees that provides a reliable latent state estimate from a history of proprioceptive measurements. This stable estimate initializes a computationally efficient predictor, designed for the rapid, parallel evaluation of thousands of potential trajectories required by modern sampling-based planners. We validated the system by integrating our neural predictor into an MPPI-based planner on a Vision 60 quadruped. Hardware experiments successfully demonstrated effective, limb-aware motion planning in a challenging, narrow passage and over small objects, highlighting our system's ability to provide a robust foundation for high-performance, collision-aware planning on dynamic robotic platforms.

Learning Neural Observer-Predictor Models for Limb-level Sampling-based Locomotion Planning

TL;DR

The paper tackles safe, limb-aware locomotion planning by learning a full-body motion predictor anchored by a provably stable neural observer. A decoupled observer-predictor architecture recovers latent states from history and offers a fast GRU-based predictor capable of parallel trajectory rollouts, enabling real-time MPPI planning with limb-level collision checks. The authors introduce joint end-to-end training with a contraction-based stability term, build robust robocentric datasets from simulation and real hardware, and demonstrate significant improvements in goal-pose tracking and collision avoidance on the Vision60 quadruped. Hardware experiments show real-time planning at 25 Hz with thousands of trajectory evaluations, outperforming a traditional kinematic baseline in cluttered environments. The approach provides a scalable, safety-guaranteed foundation for high-performance, collision-aware planning in dynamic legged robots.

Abstract

Accurate full-body motion prediction is essential for the safe, autonomous navigation of legged robots, enabling critical capabilities like limb-level collision checking in cluttered environments. Simplified kinematic models often fail to capture the complex, closed-loop dynamics of the robot and its low-level controller, limiting their predictions to simple planar motion. To address this, we present a learning-based observer-predictor framework that accurately predicts this motion. Our method features a neural observer with provable UUB guarantees that provides a reliable latent state estimate from a history of proprioceptive measurements. This stable estimate initializes a computationally efficient predictor, designed for the rapid, parallel evaluation of thousands of potential trajectories required by modern sampling-based planners. We validated the system by integrating our neural predictor into an MPPI-based planner on a Vision 60 quadruped. Hardware experiments successfully demonstrated effective, limb-aware motion planning in a challenging, narrow passage and over small objects, highlighting our system's ability to provide a robust foundation for high-performance, collision-aware planning on dynamic robotic platforms.
Paper Structure (27 sections, 2 theorems, 29 equations, 9 figures, 1 table, 1 algorithm)

This paper contains 27 sections, 2 theorems, 29 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction and Related Work
  2. System Overview
  3. Problem Statement
  4. Decoupled Observer-Predictor Architecture
  5. Joint End-to-End Training
  6. MPPI Planning
  7. Learning Observer and Predictor
  8. Building Datasets
  9. Loss Function
  10. Model Analysis
  11. MPPI Planing for Goal-Pose Navigation
  12. Cost Function
  13. Stability Analysis of the Neural Observer
  14. Lipschitz Continuity of MLP
  15. UUB Guarantee via Contraction Analysis
  16. ...and 12 more sections

Key Result

Lemma V.2

Let $g(\mathbf x)= \mathbf W^{N+1}\phi\bigl(\mathbf W^{N}(\cdots \phi(\mathbf W^{1} \mathbf x+\mathbf b^{1})\cdots)+\mathbf b^{N}\bigr),$ where each $\mathbf W^{n}$ is a matrix, $\mathbf b^{n}$ a bias vector, and $\phi(\mathbf x)=\max\{\mathbf x,0\}$ is applied element-wise. Then an upper bound on t

Figures (9)

  • Figure 1: The pipeline of the proposed system. The dataset is collected from both simulation and real robots and used to jointly train the proposed observer-predictor. The trained predictor is then deployed into the sampling-based MPPI planner for safe navigation. Full-body prediction allows for limb-level collision checking in narrow passages and over small objects.
  • Figure 2: The proposed decoupled observer-predictor architecture. Our framework consists of a correction-based nonlinear observer (left) that produces a stable latent state estimate $\hat{\mathbf x}_k$ from history. This state initializes a recurrent predictor (right) that unrolls future relative full-body configurations $\hat{\mathbf z}'$ in response to a candidate command sequence.
  • Figure 3: Training Behaviors. Comparison of training with (blue) and without (orange) the stability regularization term \ref{['eq:stability_loss']}. The stabilized model maintains the contraction factor $\rho$ strictly below unity, leading to smoother convergence and lower variance, while the unconstrained model quickly becomes unstable.
  • Figure 4: Test Performance. (top) Observer state estimation error converges rapidly from a large initial error distribution. (bottom) The resulting predictor rollout error remains low and bounded over the full 4-second horizon, demonstrating accurate long-term forecasting.
  • Figure 5: Robot Occupancy Predictor. An ReLU MLP-based occupancy predictor, with layer sizes $[64,128]$, takes joint angles $\bm\theta_k$ as input and outputs a $780$ set of points ${}^{B}\mathcal{O}(\bm\theta_k)$ representing occupied space in the robot's base frame. For collision checking, these points are transformed to the global frame and compared against an environment map $\mathcal{M}$.
  • ...and 4 more figures

Theorems & Definitions (5)

  • Definition V.1: Lipschitz Continuity Khalil2002PH
  • Lemma V.2: Lipschitz constant of ReLU MLP Virmaux2018ANIPS
  • proof : Proof sketch
  • Theorem V.3: UUB of Observer Error
  • proof : Proof sketch