# PLOP: Probabilistic poLynomial Objects trajectory Planning for autonomous driving

arXiv: https://arxiv.org/abs/2003.08744 · HTML: https://mlsanity.com/paper/2003.08744/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 19 of 19)

- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [Stepwise Goal-Driven Networks for Trajectory Prediction](https://mlsanity.com/paper/2103.14107/) (2021)
- [Occupancy Flow Fields for Motion Forecasting in Autonomous Driving](https://mlsanity.com/paper/2203.03875/) (2022)
- [HIMap: HybrId Representation Learning for End-to-end Vectorized HD Map Construction](https://mlsanity.com/paper/2403.08639/) (2024)
- [SIMPL: A Simple and Efficient Multi-agent Motion Prediction Baseline for Autonomous Driving](https://mlsanity.com/paper/2402.02519/) (2024)
- [VisionTrap: Vision-Augmented Trajectory Prediction Guided by Textual Descriptions](https://mlsanity.com/paper/2407.12345/) (2024)
- [OccFeat: Self-supervised Occupancy Feature Prediction for Pretraining BEV Segmentation Networks](https://mlsanity.com/paper/2404.14027/) (2024)
- [StopNet: Scalable Trajectory and Occupancy Prediction for Urban Autonomous Driving](https://mlsanity.com/paper/2206.00991/) (2022)
- [Narrowing the Coordinate-frame Gap in Behavior Prediction Models: Distillation for Efficient and Accurate Scene-centric Motion Forecasting](https://mlsanity.com/paper/2206.03970/) (2022)
- [Improving Out-of-Distribution Generalization of Trajectory Prediction for Autonomous Driving via Polynomial Representations](https://mlsanity.com/paper/2407.13431/) (2024)
- [MoST: Multi-modality Scene Tokenization for Motion Prediction](https://mlsanity.com/paper/2404.19531/) (2024)
- [Raising context awareness in motion forecasting](https://mlsanity.com/paper/2109.08048/) (2021)
- [Neuroevolutionary Multi-objective approaches to Trajectory Prediction in Autonomous Vehicles](https://mlsanity.com/paper/2205.02105/) (2022)
- [An Empirical Bayes Analysis of Object Trajectory Representation Models](https://mlsanity.com/paper/2211.01696/) (2022)
- [Trajectory Forecasting on Temporal Graphs](https://mlsanity.com/paper/2207.00255/) (2022)
- [Conformal Trajectory Prediction with Multi-View Data Integration in Cooperative Driving](https://mlsanity.com/paper/2408.00374/) (2024)

## Abstract (arXiv)

To navigate safely in urban environments, an autonomous vehicle (ego vehicle) must understand and anticipate its surroundings, in particular the behavior and intents of other road users (neighbors). Most of the times, multiple decision choices are acceptable for all road users (e.g., turn right or left, or different ways of avoiding an obstacle), leading to a highly uncertain and multi-modal decision space. We focus here on predicting multiple feasible future trajectories for both ego vehicle and neighbors through a probabilistic framework. We rely on a conditional imitation learning algorithm, conditioned by a navigation command for the ego vehicle (e.g., "turn right"). Our model processes ego vehicle front-facing camera images and bird-eye view grid, computed from Lidar point clouds, with detections of past and present objects, in order to generate multiple trajectories for both ego vehicle and its neighbors. Our approach is computationally efficient and relies only on on-board sensors. We evaluate our method offline on the publicly available dataset nuScenes, achieving state-of-the-art performance, investigate the impact of our architecture choices on online simulated experiments and show preliminary insights for real vehicle control