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Prediction uncertainty-aware planning using deep ensembles and trajectory optimisation

Anshul Nayak, Azim Eskandarian

TL;DR

This work addresses safe social navigation under stochastic human motion by coupling deep ensemble-based probabilistic trajectory prediction with an NMPC planner that incorporates predictive uncertainty as constraints. The approach compares hard collision constraints, linear chance constraints, and control barrier functions within a receding-horizon optimization, evaluated on ETH/UCY datasets and real-world out-of-distribution corridors. Key contributions include a modular prediction-planning pipeline, a formal uncertainty decomposition (aleatoric vs. epistemic) via deep ensembles, and a comprehensive comparison of constraint strategies showing that CBF and chance constraints yield safer, more efficient navigation than hard constraints in pedestrian-rich or constrained environments. The results demonstrate practical impact for proactive and robust robot navigation in dynamic human crowds, with future work focusing on cooperative planning where humans adapt to robot behavior.

Abstract

Human motion is stochastic and ensuring safe robot navigation in a pedestrian-rich environment requires proactive decision-making. Past research relied on incorporating deterministic future states of surrounding pedestrians which can be overconfident leading to unsafe robot behaviour. The current paper proposes a predictive uncertainty-aware planner that integrates neural network based probabilistic trajectory prediction into planning. Our method uses a deep ensemble based network for probabilistic forecasting of surrounding humans and integrates the predictive uncertainty as constraints into the planner. We compare numerous constraint satisfaction methods on the planner and evaluated its performance on real world pedestrian datasets. Further, offline robot navigation was carried out on out-of-distribution pedestrian trajectories inside a narrow corridor

Prediction uncertainty-aware planning using deep ensembles and trajectory optimisation

TL;DR

This work addresses safe social navigation under stochastic human motion by coupling deep ensemble-based probabilistic trajectory prediction with an NMPC planner that incorporates predictive uncertainty as constraints. The approach compares hard collision constraints, linear chance constraints, and control barrier functions within a receding-horizon optimization, evaluated on ETH/UCY datasets and real-world out-of-distribution corridors. Key contributions include a modular prediction-planning pipeline, a formal uncertainty decomposition (aleatoric vs. epistemic) via deep ensembles, and a comprehensive comparison of constraint strategies showing that CBF and chance constraints yield safer, more efficient navigation than hard constraints in pedestrian-rich or constrained environments. The results demonstrate practical impact for proactive and robust robot navigation in dynamic human crowds, with future work focusing on cooperative planning where humans adapt to robot behavior.

Abstract

Human motion is stochastic and ensuring safe robot navigation in a pedestrian-rich environment requires proactive decision-making. Past research relied on incorporating deterministic future states of surrounding pedestrians which can be overconfident leading to unsafe robot behaviour. The current paper proposes a predictive uncertainty-aware planner that integrates neural network based probabilistic trajectory prediction into planning. Our method uses a deep ensemble based network for probabilistic forecasting of surrounding humans and integrates the predictive uncertainty as constraints into the planner. We compare numerous constraint satisfaction methods on the planner and evaluated its performance on real world pedestrian datasets. Further, offline robot navigation was carried out on out-of-distribution pedestrian trajectories inside a narrow corridor

Paper Structure

This paper contains 18 sections, 25 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Uncertainty-Inclusive Trajectory Prediction
  4. Probabilistic Trajectory Prediction
  5. Deep Ensembles
  6. Uncertainty Estimation
  7. Architecture
  8. Prediction Uncertainty-Aware Planning
  9. Robot and Obstacle Model
  10. Hard Collision Constraint
  11. Linear Chance Constraint
  12. Control Barrier Function
  13. Receding Horizon Planning
  14. Experiments
  15. Implementation Details
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Uncertainty-aware planning using MPC-CBF with a forecast horizon of 8 steps. At t = 2 secs, the robot proactively changes its heading to avoid collision with the oncoming pedestrians. At t = 6 secs, the robot slows down as it is unable to find a feasible path to goal without hitting the pedestrian. At t =10 secs, the robot starts to move as soon as the pedestrian crosses.
  • Figure 2: Prediction uncertainty-aware offline robot navigation with a single pedestrian. At t = 2.4 secs, the robot has proactively found an optimal path to goal with a large N = 12. At t = 3.6 secs, the robot navigates ensuring a minimum distance of 0.89m.
  • Figure 3: Robot navigation with multiple pedestrians. Between 1.2 secs and 2.4 secs, the robot is unable to find a feasible path and even moves backward to satisfy the constraints. At t=3.6 secs, the robot manages to find a path towards goal and at t=4.8 secs, the robot avoids collision with the pedestrian while maintaining a safety margin of 0.18 m.