Fast and Accurate Multi-Agent Trajectory Prediction For Crowded Unknown Scenes

TL;DR

The paper tackles the challenge of real-time, accurate multi-agent trajectory prediction in unknown crowded environments. It proposes an energy-function optimization framework that combines a streamlined interaction term, Frechet-distance-based online group division, and a decoupled optimization approach solved with a Salp Swarm Algorithm and gradient-descent refinement. A similarity-based resample evaluation (SRE) method estimates agents' target headings, enabling online trajectory prediction without offline destination learning. Empirical results on ETH, HOTEL, UNIV, ZARA1, and ZARA2 datasets demonstrate competitive accuracy and real-time performance, including predictions for 20 pedestrians within 0.8 seconds. Overall, the approach provides a robust, dataset-free, online framework suitable for autonomous navigation in unknown crowded scenes.

Abstract

This paper studies the problem of multi-agent trajectory prediction in crowded unknown environments. A novel energy function optimization-based framework is proposed to generate prediction trajectories. Firstly, a new energy function is designed for easier optimization. Secondly, an online optimization pipeline for calculating parameters and agents' velocities is developed. In this pipeline, we first design an efficient group division method based on Frechet distance to classify agents online. Then the strategy on decoupling the optimization of velocities and critical parameters in the energy function is developed, where the the slap swarm algorithm and gradient descent algorithms are integrated to solve the optimization problems more efficiently. Thirdly, we propose a similarity-based resample evaluation algorithm to predict agents' optimal goals, defined as the target-moving headings of agents, which effectively extracts hidden information in observed states and avoids learning agents' destinations via the training dataset in advance. Experiments and comparison studies verify the advantages of the proposed method in terms of prediction accuracy and speed.

Figures (15)

• Figure 1: Interaction parameters of agent $i$. ${\rm v}_{t}^i$ and ${\rm v}_{t}^j$ are velocities of agents $i$ and $j$, respectively. ${\rm R}_d$ is the detection distance of the sensor on agent $i$, and ${\rm R}_d \ge {\sigma _w^i}$. When agent $i$ moves from ${\bf{p}}_{t}^i$ to ${\bf{p}}_{t+1}^i$, the distance between agents $i$ and $j$ is ${\sigma _w^i}$. To avoid the collision, agent $i$ needs to change its motions. At time $t+2$, agent $i$ maintains the minimal distance ${\sigma _d^i}$ from $j$ to keep its safety.
• Figure 2: Cost distributions of interaction functions with selecting velocity ${\bf{v}}_{t + 1}^i$. ${\bf{p}}_t^i$ and ${\bf{p}}_t^j$ are positions of agents $i$ and $j$ at time $t$, the yellow arrow lines represent the velocity of agent $j$, the black circles are the velocity constraint of ${\bf{v}}^i$, which is $\left\| {{{\bf{v}}^i}} \right\| \leq 2.5$, the blue arrow lines ${\bf{v}}_{min}^i$ represent selected velocities ${\bf{v}}_{t + 1}^i$, which correspond to minimum values of ${\rm{E}}_{collision}(\cdot)$ and ${\rm{E'}}_{collision}(\cdot)$, the black arrow lines ${\bf{v}}_{max}^i$ are selected velocities ${\bf{v}}_{t + 1}^i$, which correspond to maximum values of ${\rm{E}}_{collision}(\cdot)$ and ${\rm{E'}}_{collision}(\cdot)$. (a) Interaction function ${\rm{E}}_{collision}(\cdot)$ with parameters ${\sigma _d^i}$, ${\sigma _w^i}$, and $\beta^i$. (b) Interaction function ${\rm{E'}}_{collision}(\cdot)$ with parameters ${{\rm{w}}^i}$, ${{\rm d}^i}$, and ${\alpha ^i}$.
• Figure 3: Scheme of the proposed trajectory prediction method.
• Figure 4: The discrete Frechet distance and the similarity comparing. (a) The process of calculating the discrete Frechet distance between two point sets. The black and blue arrow curves are two paths, and the points on the curves are sampled path nodes. To calculate the discrete Frechet distance, there display two mapping modes, $a_k$ and $b_k$, which are connected by cyan lines and red dashed lines, for example. In the mapping mode with cyan line, ${\rm N}=5$ and the value of \ref{['E17_maxDis']} is $d_1$, which is the distance between ${\bf{p}}_{1,4}$ and ${\bf{p}}_{2,2}$. As the mapping mode with red dashed lines, ${\rm N}=6$ and the value of \ref{['E17_maxDis']} is ${d_2} = \left\| {{{\bf{p}}_{1,6}} - {{\bf{p}}_{2,7}}} \right\|$. ${\delta _{{\rm{dF}}}}$ is the discrete Frechet distance, which is the distance between ${\bf{p}}_{1,5}$ and ${\bf{p}}_{2,5}$, under the given sampled path nodes. (b) The comparison of paths' similarities by the Frechet distance. The double arrow dashed lines represent values of the Frechet distances corresponding to compared paths. The Frechet distance ${\delta _{{\rm{dF}}}^{1,2}}$ of path 1 and path 2 is the smallest, and the Frechet distances between path 4 to the other three paths are larger than ${\delta _{{\rm{dF}}}^{1,2}}$, ${\delta _{{\rm{dF}}}^{1,3}}$ and ${\delta _{{\rm{dF}}}^{2,3}}$. (c) The similarities of paths with the Frechet distances in (b), the smaller value the higher similarity.
• Figure 5: The workflow of Algorithm\ref{['Alg1_group']}.