Citation: Hoang-Dinh, K.; Leibold,
M.; Wollherr, D. A Fast and
Close-to-Optimal Receding Horizon
Control for Trajectory Generation in
Dynamic Environments. Robotics
2022, 11, 72. https://doi.org/
10.3390/robotics11040072
Academic Editor: Dario Richiedei
Received: 30 May 2022
Accepted: 4 July 2022
Published: 6 July 2022
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Article
A Fast and Close-to-Optimal Receding Horizon Control for
Trajectory Generation in Dynamic Environments
Khoi Hoang-Dinh
1,
*
,†
, Marion Leibold
2,†
and Dirk Wollherr
2,†
1
Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, No. 12 Nguyen Van Bao,
Ward 4, Go Vap District, Ho Chi Minh City 70000, Vietnam
2
Automatic Control Engineering, Technische Universität München, 80333 München, Germany;
marion.leibold@tum.de (M.L.); dw@tum.de (D.W.)
* Correspondence: hoangdinhkhoi@iuh.edu.vn
† These authors contributed equally to this work.
Abstract:
This paper presents a new approach for the optimal trajectory planning of nonlinear systems
in a dynamic environment. Given the start and end goals with an objective function, the problem is
to find an optimal trajectory from start to end that minimizes the objective while taking into account
the changes in the environment. One of the main challenges here is that the optimal control sequence
needs to be computed in a limited amount of time and needs to be adapted on-the-fly. The control
method presented in this work has two stages: the first-order gradient algorithm is used at the
beginning to compute an initial guess of the control sequence that satisfies the constraints but is not
yet optimal; then, sequential action control is used to optimize only the portion of the control sequence
that will be applied on the system in the next iteration. This helps to reduce the computational effort
while still being optimal with regard to the objective; thus, the proposed approach is more applicable
for online computation as well as dealing with dynamic environments. We also show that under mild
conditions, the proposed controller is asymptotically stable. Different simulated results demonstrate
the capability of the controller in terms of solving various tracking problems for different systems
under the existence of dynamic obstacles. The proposed method is also compared to the related
indirect optimal control approach and sequential action control in terms of cost and computation
time to evaluate the improvement of the proposed method.
Keywords:
optimal control; trajectory generation; robotics; receding horizon control; model predictive
control; dynamic environments; simulation results
1. Introduction
Trajectory planning in robotics and automation has attracted a great deal of attention
recently due to the new demands in this area. Besides reaching the goal, it is crucial that
the controlled robot is able to react to highly dynamic environments, e.g., avoiding vehicles
and pedestrians in the case of autonomously driving cars, or avoiding human co-workers
to provide safety in the case of humans and robots working in the same workspace. This
requires the robot to adapt rapidly to changing situations. Furthermore, it is desired that,
besides safety, also other demands are considered, such as optimizing energy and human
comfort, etc. Solving trajectory planning problems while taking all of these aspects into
consideration is not a trivial task.
In general, the trajectory planning problem is either solved on a kinematic or dynamic
level. On the kinematic level, the outcome of trajectory planning is a set of waypoints;
each consists of a time stamp and the position/velocity/acceleration of the system. Then,
a controller, i.e., a PID controller, is used to generate a control signal applied to the sys-
tem. In this area, different planning techniques were first presented in automated vehicle
demonstrations [1–3].
One of the first techniques was the use of interpolating curve plan-
ners, i.e., with the use of clothoid paths in the Eureka Prometheus Project [
4
] between
1987 and 1994, where the transitions between linear parts and curves are achieved with
Robotics 2022, 11, 72. https://doi.org/10.3390/robotics11040072 https://www.mdpi.com/journal/robotics
