Learning to Predict Vehicle Trajectories with
Modelbased Planning
In Submission
Abstract
Predicting the future trajectories of onroad vehicles is critical for autonomous driving. In this paper, we introduce a novel prediction framework called PRIME, which stands for Prediction with Modelbased Planning. Unlike recent prediction works that utilize neural networks to model scene context and produce unconstrained trajectories, PRIME is designed to generate accurate and feasibilityguaranteed future trajectory predictions, which guarantees the trajectory feasibility by exploiting a modelbased generator to produce future trajectories under explicit constraints and enables accurate multimodal prediction by using a learningbased evaluator to select future trajectories. We conduct experiments on the largescale Argoverse Motion Forecasting Benchmark. Our PRIME outperforms stateoftheart methods in prediction accuracy, feasibility, and robustness under imperfect tracking. Furthermore, we achieve the 1st place on the Argoverse Motion Forecasting Leaderboard.
Motivation & Key idea
In traffic scenarios, most vehicles operate under their inherent kinematic constraints (e.g., nonholonomic motion constraints for vehicles)
while in compliance with the road structure (e.g., lane connectivity, static obstacles)
and semantic information (e.g., traffic lights, speed limits).
All these kinematic and environmental constraints explicitly regularize the trajectory space.
However, most existing future prediction approaches model traffic agents as points and produce sequences of future positions without constraints.
Such constraintfree predictions may be incompliant with kinematic or environmental characteristics,
which gives rise to massive uncertainty in the predicted future states.
Consequently, the downstream planning module would inevitably undergo some extra burdens and even the "freezing robot problem."
Moreover, the recent learningbased prediction models follow the typical paradigm of generating trajectory predictions by network regression that highly relies on longterm tracking results.
But for some dense driving scenarios where the target would be momently occluded or suddenly appears within the sensing range, tracking results are discontinuous or not accumulated enough.
The prediction accuracy would degrade under such imperfect tracking cases.
Toward overcoming these challenges, we propose a novel prediction architecture called PRIME.
The critical idea is to exploit a modelbased motion planner as the prediction generator to sample feasible future trajectories under explicit constraints,
together with a deep neural network as the prediction evaluator to model implicit interactions and select future trajectories by scoring.
The novel architecture contributes to accurate, feasible, and robust trajectory predictions.
More specifically,
the modelbased generator (left) which samples the target's feasible future trajectories \(\mathcal{T}\)
by taking its realtime state \(\mathbf{s}_{tar}^0\) and the map \(\mathcal{M}\),
while explicitly imposing kinematical and environmental constraints to guarantee trajectory feasibility;
the learningbased evaluator (right) which receives the feasible trajectories \(\mathcal{T}\) and all observed tracks \(\mathcal{S}\)
to model the implicit interactions among all traffic agents, and selects a final set of feasible trajectories \(\mathcal{T}_{tar}\subset\mathcal{T}\) as the prediction result.
Framework Overview
The modelbased generator searches reachable paths \(\mathcal{P}\) through the map with DepthFirstSearch
and samples a set of feasible future trajectories \(\mathcal{T}\) with the Frenet Planer.
This part is detailed in our paper.
The learningbased evaluator first encodes scene context given by \((\mathcal{P}, \mathcal{T}, \mathcal{S})\),
including \(l\) paths in \(\mathcal{P}\), \((m+1)\) history tracks in \(\mathcal{S}\) and \(n\) future trajectories in \(\mathcal{T}\).
The implicit agentmap interactions are learned in the subsequent attention modules:
P2T and P2F propagate the spatial information of each reference path \(\mathcal{P}_i\) into history tracks and corresponding future trajectories,
and A2A takes track tensors from P2T to capture the multiagent interactions.
As the pathbased Frenet coordinate is used in our dual spatial representation, P2T, P2F, and A2A operate for each path,
while F2F fuses all the future trajectories processed by P2F to obtain a global understanding for the reachable space.
Subsequently, each feasible trajectory \(\mathcal{T}_{j,k}\) could query its track tensor \(\mathbf{X}_j(\mathbf{s}_{tar})\) from P2T,
interaction tensor \(\mathbf{Y}_j(\mathbf{s}_{tar})\) from A2A and future tensor \(\mathbf{Z}(\mathcal{T}_{j,k})\) from F2F,
and it is scored by feeding the concatenation of these tensors to fullyconnected layers.
Finally, the evaluator ranks all feasible future trajectories in \(\mathcal{T}\) by scoring and outputs a final set of \(K\) predicted trajectories.
Quantitative Results
Qualitative Results
Qualitative results under various scenarios on the Argoverse validation set. The modelbased generator produces the set of future trajectories \(\mathcal{T}\) (blue) with feasibility guaranteed, which well regularize the target vehicle's future trajectory space. The learningbased evaluator selects \(K\) trajectories from \(\mathcal{T}\) as multimodal prediction results (red), and the depth of red indicates their probability.







[Supp. 1] Comparison with Fully Learningbased Prediction
Compared with the mainstream learningbased methods that generate unconstrained trajectory predictions by neural networks, the main difference of our proposed PRIME framework is to explicitly constrain the prediction space and thereby ensure trajectory feasibility. Here, we use LaneGCN as a representative for the typical fully learningbased prediction models, and among the current stateoftheart methods, it is opensource. We demonstrate some common failures of kinematically and environmentally infeasible predictions in the following.
Due to kinematic constraints, vehicles cannot take a sudden turn at high speed (1strow in Fig. 6), or reverse the moving direction (2ndrow in Fig. 6). Also, the prediction results of turning with across lane boundaries (1strow in Fig.7), or heading towards reverse lanes (2ndrow in Fig.7) are incompliant with environmental constraints. Moreover, the counterintuitive bidirectional trajectories predicted by LaneGCN (2ndrow in Fig.7) also reveal that the fully learningbased prediction relies on relative longrange tracks for regressing trajectories, but it may degrade under shortrange tracks.
In some of the above examples, although it looks PRIME and LaneGCN show comparable performance when evaluated by minADE\(_6\) and minFDE\(_6\), their impacts on the downstream planning differ a lot. The infeasible trajectories generated by LaneGCN bring massive uncertainty in the predicted future states, which would cause redundant burdens for an autonomous vehicle to make decisions and motion plans. Especially in dense traffic where multiple surrounding vehicles need to be predicted, the negative impact of infeasible predictions would be further aggravated. By contrast, PRIME regularizes the future trajectory space (blue) by given constraints and thus makes accurate and reasonable future predictions (red).
[Supp. 2] Impacts Caused by Defect Data
Although Argoverse is one of the most recognized benchmarks for trajectory prediction due to its highquality trajectory and map annotation, some of its ground truth trajectories are not completely correct. The common issues result from the tracking method used for annotating the data, including position oscillation (Fig. 8(a)) and id switch (Fig. 8(b)) that the ground truth trajectory is suddenly switched to a neighboring agent. Such defect cases would lead to worse performance indicators (ADE/FDEbased metrics) of our method in the quantitative evaluation, but it is evident that the smooth trajectories predicted by PRIME are more realistic and reasonable.
[Supp. 3] Failure Cases
We demonstrate the failure cases of our method on the Argoverse validation set in Fig. 9. The failures are mostly related to the estimation deviation for the target vehicle's current state \(\mathbf{s}_{tar}^0\). Although the samplingbased strategy in our generator could compensate for inaccurate state estimation to some extent, estimating the heading and velocity from sequences of centroid positions would be intractable when there exists serious data noise. For example, the position oscillation of a shortdistance history track would make the heading direction hard to estimate, as shown in Fig. 9(a). As a result, the ground truth trajectory locates out of the resulted prediction space's span range. When the position sequence vibrates too much, the accuracy of velocity estimation would even be affected. As exemplified in Fig. 9(b), the future trajectory space does not cover the ground truth trajectory due to the inaccurate estimation for the target's low velocity, leading to a relatively large displacement error in the prediction results.
Nonetheless, the accuracy of state estimation could be improved by incorporating more information. For instance, the vehicle's bounding box given by detection provides geometry information in addition to discrete positions, which would enable more robust and accurate state estimation for prediction targets.
Runtime Analysis
The inference frequency of our prediction framework depends on the scene complexity, sampling density, and computing power. Running with Intel i77820X, the generation of a single trajectory with a single thread spends 0.1~0.2 ms on average. With each trajectory sample produced independently, the modelbased trajectory generator could be highly parallelized to provide full coverage to the future prediction space with satisfactory realtime performance. For the learningbased evaluator, it is implemented by a lightweight network with only 1.02 million parameters. Its inference time on NVIDIA 2080TI is 8~12 ms. Overall, the whole framework of PRIME could well satisfy the realtime requirements for autonomous driving.
BibTeX
@article{song2021learning, title={Learning to Predict Vehicle Trajectories with Modelbased Planning}, author={Song, Haoran and Luan, Di and Ding, Wenchao and Wang, Michael Yu and Chen, Qifeng}, journal={arXiv preprint arXiv:2103.04027}, year={2021} }