
Trajectory modification considering dynamic constraints
of autonomous robots
Christoph Rösmann, Wendelin Feiten, Thomas Wösch
Siemens Corporate Technology, Intelligent Systems and Control, Germany
Frank Hoffmann, Torsten Bertram
Institute of Control Theory and Systems Engineering, Technische Universität Dortmund, Germany
Topic: Research and Development / modelling, planning and control
Keywords: Trajectory modification, timed elastic band, dynamics, kinematics, autonomous robots
Abstract
The classic "elastic band" deforms a path generated by a global planner with respect to the shortest path length while
avoiding contact with obstacles. It does not take any dynamic constraints of the underlying robot into account directly.
This contribution introduces a new approach called "timed elastic band" which explicitly considers temporal aspects of
the motion in terms of dynamic constraints such as limited robot velocities and accelerations. The "timed elastic band"
problem is formulated in a weighted multi-objective optimization framework. Most objectives are local as they depend
on a few neighboring intermediate configurations. This results in a sparse system matrix for which efficient large-scale
constrained least squares optimization methods exist.
Results from simulations and experiments with a real robot demonstrate that the approach is robust and computationally
efficient to generate optimal robot trajectories in real time. The "timed elastic band" converts an initial path composed of
a sequence of way points into a trajectory with explicit dependence on time which enables the control of the robot in real
time. Due to its modular formulation the approach is easily extended to incorporate additional objectives and constraints.
1 Introduction
Motion planning is concerned with finding of a collision
free trajectory that respects the kinematic and dynamic mo-
tion constraints.
In the context of motion planning this paper focuses on
local path modification assuming that an initial path has
been generated by a global planner [1]. In particular in the
context of service robotics the modification of a path is a
preferable approach due to the inherent uncertainty of the
dynamic environment since the environment may be dy-
namic. Also, the model of the environment may subject to
change due to partial, incomplete maps and dynamic ob-
stacles. Furthermore, the (re-)computation of a large scale
global path is often not feasible in real-time applications.
This observation leads to approaches which modify a path
locally, such as the "elastic band" proposed by [2, 3]. The
main idea of the "elastic band" approach is to deform an
originally given path by considering it as an elastic rubber
band subject to internal and external forces which balance
each other in the attempt to contract the path while keeping
a distance from obstacles.
Later this approach was extended to non-holonomic kine-
matics [4, 5, 6], robotic systems with many degrees of free-
dom [7] and dynamics obstacles [8]. However, to our best
knowledge dynamic motion constraints have not yet been
considered as an objective in path deformation. The typical
approach is to smoothen the path for example with splines
to obtain dynamically feasible trajectories.
Path PlanningWorld Model
Position &
Velocity
Task
Robot
&
Environment
Local
Obstacles
Control
Trajectory
Generation &
Modification
Timed Elastic Band
Figure 1: Robot system with "timed elastic band"
Our approach, called "timed elastic band" is novel as it
explicitly augments "elastic band" with temporal informa-
tion, thus allowing the consideration of the robot’s dy-
namic constraints and direct modification of trajectories
rather than paths. Figure 1 shows the architecture of a
robot system with the "timed elastic band". By considering
the temporal information, the "timed elastic band" can be
used to control also the velocites and accelerations of the
robot. The new approach is suitable for high dimensional
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