Probabilistically Safe Robot Planning with Confidence-Based Human Predictions

Jaime F. Fisac, Andrea Bajcsy, Sylvia L. Herbert, David Fridovich-Keil, Steven Wang, Claire J. Tomlin, Anca D. Dragan

Seminal May 2018

TL;DR A robot treats the rationality coefficient of its human-motion model as a measure of confidence in that model, infers it online, and plans around the resulting predictions with a 1% collision-probability limit. On 48 recorded walking trajectories, this kept a simulated quadcopter farther from people or got it to its goal sooner than fixed-confidence predictions when the person avoided an unmodeled obstacle or headed to an unmodeled goal.

What they do

A robot that predicts human motion with a goal-directed model can get dangerously close when the person does something the model does not explain, such as stepping around a spill the robot does not know about. This paper reads the rationality coefficient β of a noisily rational (Boltzmann) human model as the robot’s confidence in that model and infers it in real time. The resulting predictions feed a planner that comes with a probabilistic safety certificate. The running example is a quadcopter flying to goals in a room where a person walks.

How it works

Confidence inference. Each observed human action updates a Bayesian belief over about 10 log-spaced β values, optionally jointly with a belief over the person’s goal. Low β spreads the predicted actions toward uniform; high β trusts the model.
Prediction. The belief is propagated through the human dynamics to get a distribution over future human positions at each time step.
Safe planning. FaSTrack uses Hamilton-Jacobi reachability to precompute a worst-case tracking-error bound around any planned trajectory. The planner rejects a trajectory point if the human probability mass that could collide with the padded robot exceeds 1%. Using the highest per-step probability for the whole trajectory errs on the optimistic side; continual replanning is meant to make up for this.

Results

Setup: 48 walking trajectories from 16 people (OptiTrack, about 235 Hz), replayed against a simulated quadcopter in three environments. The baselines fix β at 0.05 (low confidence) or 10 (high confidence).
Complete model (straight walk to a known goal): all three methods perform comparably in safety and efficiency.
Unmodeled obstacle: β inference keeps a larger minimum distance and reaches the goal faster than both baselines.
Unmodeled goal: similar minimum distance for all three, with β inference several seconds faster.

Limitations

The model assumes a single human who does not react to the robot. The trajectory collision probability is an optimistic approximation. The quantitative results come from simulated flights against recorded trajectories; the Crazyflie 2.0 hardware demonstration reports no numbers. The authors leave more complex motion, closed-loop interaction and multiple humans to future work.

Videos

Figures

From Figure 1: A quadcopter plans around the predicted occupancy of a walking person. With fixed model confidence, th... — From Figure 1: A quadcopter plans around the predicted occupancy of a walking person. With fixed model confidence, the prediction misses the person avoiding an obstacle and the robot comes close to them (left); updating model confidence in real time widens the prediction and the robot keeps clear (right).

From Figure 2: Predicted human occupancy as a person walks from the bottom right to a goal (red circle, top row) or d... — From Figure 2: Predicted human occupancy as a person walks from the bottom right to a goal (red circle, top row) or detours around a spill on the floor (bottom row), under low, high and Bayesian-inferred model confidence.

From Figure 4: Robot trajectories in the spill scenario. With low confidence the robot deviates far from its path; wi... — From Figure 4: Robot trajectories in the spill scenario. With low confidence the robot deviates far from its path; with high confidence it keeps its course and comes dangerously close to the person; with inferred confidence it makes a slight detour.

From Figure 5: Minimum human-robot distance (safety) and the robot's time to goal relative to the low- and high-confi... — From Figure 5: Minimum human-robot distance (safety) and the robot's time to goal relative to the low- and high-confidence baselines (efficiency), with a complete model and with an unmodeled obstacle.

Abstract

In order to safely operate around humans, robots can employ predictive models of human motion. Unfortunately, these models cannot capture the full complexity of human behavior and necessarily introduce simplifying assumptions. As a result, predictions may degrade whenever the observed human behavior departs from the assumed structure, which can have negative implications for safety. In this paper, we observe that how "rational" human actions appear under a particular model can be viewed as an indicator of that model's ability to describe the human's current motion. By reasoning about this model confidence in a real-time Bayesian framework, we show that the robot can very quickly modulate its predictions to become more uncertain when the model performs poorly. Building on recent work in provably-safe trajectory planning, we leverage these confidence-aware human motion predictions to generate assured autonomous robot motion. Our new analysis combines worst-case tracking error guarantees for the physical robot with probabilistic time-varying human predictions, yielding a quantitative, probabilistic safety certificate. We demonstrate our approach with a quadcopter navigating around a human.

Summaries are written automatically from each paper's text. Figures and videos come from the paper and its project page; all credit goes to the authors.

Matt Strong