IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED DECEMBER, 2019 1
Online Trajectory Generation with Distributed
Model Predictive Control for Multi-Robot Motion
Planning
Carlos E. Luis
1
, Marijan Vukosavljev
1
and Angela P. Schoellig
1
Abstract—We present a distributed model predictive control
(DMPC) algorithm to generate trajectories in real-time for multi-
ple robots. We adopted the on-demand collision avoidance method
presented in previous work to efficiently compute non-colliding
trajectories in transition tasks. An event-triggered replanning
strategy is proposed to account for disturbances. Our simulation
results show that the proposed collision avoidance method can
reduce, on average, around 50% of the travel time required to
complete a multi-agent point-to-point transition when compared
to the well-studied Buffered Voronoi Cells (BVC) approach.
Additionally, it shows a higher success rate in transition tasks
with a high density of agents, with more than 90% success rate
with 30 palm-sized quadrotor agents in a 18 m
3
arena. The
approach was experimentally validated with a swarm of up to
20 drones flying in close proximity.
Index Terms—Motion and Path Planning, Distributed Robot
Systems, Collision Avoidance, Model Predictive Control.
I. INTRODUCTION
O
NLINE trajectory generation is key to execute missions
in dynamic or unknown environments. In particular,
multi-robot tasks are especially challenging due to a high
number of decision-making agents sharing the same space. In
such settings, the planning algorithms must compute collision-
free and goal-oriented trajectories, taking into account the state
of the environment and neighbouring agents.
A wide variety of techniques exist to tackle the multi-
robot trajectory generation problem. First, optimization-based
techniques such as Sequential Convex Programming (SCP)
[1], [2] and Distributed Model Predictive Control (DMPC)
[3], [4] have successfully solved point-to-point trajectory
generation problems for multiple agents. Second, discrete
planning strategies such as Rapidly-exploring Random Trees
(RRT) [5] have been extended to the multi-agent case. Third, a
combination of discrete planning and continuous optimization
has been developed to coordinate multiple robots in cluttered
environments [6]. GPU-accelerated approaches can reduce the
runtime of these offline planners [7].
Manuscript received: September 10, 2019; Revised November 27, 2019;
Accepted December 18, 2019.
This paper was recommended for publication by Editor Nak Young Chong
upon evaluation of the Associate Editor and Reviewers’ comments. This work
was supported by NSERC research and equipment grants (RTI 2018-00847,
CRDPJ 528161-18, CREATE 466088), and the CFI JELF/ORF grant #33000.
1
Carlos E. Luis, Marijan Vukosavljev and Angela P. Schoellig
are with the Dynamic Systems Lab (www.dynsyslab.org), Institute
for Aerospace Studies, University of Toronto, Canada. E-mails:
{carlos.luis, mario.vukosavljev, angela.schoellig}
@robotics.utias.utoronto.ca
Digital Object Identifier (DOI): see top of this page.
Fig. 1. A ten-drone transition task through a hula-hoop solved using our
proposed online trajectory generation method. Our distributed computation
allows for real-time multi-robot motion planning, enabling complex tran-
sition tasks to be performed. A video of the performance is found at
http://tiny.cc/online-dmpc.
Real-time trajectory generation is required for quick adap-
tation in dynamic environments, but it remains challenging
to implement for robot swarms. Optimal Reciprocal Collision
Avoidance (ORCA) and all its variants have pushed towards
real-time trajectory generation [8], providing experimental
validation with various robotic platforms in planar environ-
ments [9]. A similar approach achieves collision avoidance
through the concept of Buffered Voronoi Cells (BVC) [10],
showing initial results of online trajectory generation in 2D
with multiple quadrotors operating at a fixed height. The
BVC concept has been recently used in tandem with discrete
planners [11], primarily to avoid deadlocks in scenarios where
plain BVC would get trapped and fail the task.
Robust MPC frameworks such as tube MPC have been de-
veloped for distributed multi-agent systems under uncertainty,
both with linear [12] and nonlinear [13] dynamics. Although
both approaches provide proofs and simulation results, they
are not real-time implementable with current hardware and
solver capabilities.
We present a novel real-time, multi-vehicle motion planning
framework that significantly outperforms existing methods in
terms of the success rate to complete transition tasks in agent-
dense environments. To the best of our knowledge, this paper
presents the first results on real-time motion planning for
drone swarms of up to 20 drones, executed from a single off-
board computer. The proposed algorithm is implemented in a
centralized fashion, and relies on information sharing between
arXiv:1909.05150v2 [cs.RO] 24 Jan 2020
基于优化
的技术,
如序列凸
规划(SCP
)[1]、[2
]和分布
式模型预
测控制
(DMPC)[3
]、[4],
已经成功
地解决了
多个代理
的点对点
轨迹生成
问题。
开发了离
散规划和
连续优化
的组合,
以协调杂
乱环境中
的多个机
器人[6]。
GPU加速的
方法可以
减少这些
离线规划
器的运行
时间
最优相互碰
撞避免(ORCA
)及其所有变
体都推动了
实时轨迹生
成[8],提供
了平面环境
[9]中各种机
器人平台的
实验验证。
类似的方法
通过缓冲
Voronoi细胞
(BVC)[10]的
概念实现了
避免碰撞,
显示了多个
四转子在固
定高度工作
的二维在线
轨迹产生的
初始结果。
BVC的概念最
近与离散规
划器[11]一
起使用,主
要是为了在
普通BVC被困
并无法完成
任务的场景
中避免死锁
。
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