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Trajectory Deformation Through Generalized Time Scaling

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Original languageEnglish
Title of host publication2018 European Control Conference (ECC)
Number of pages8
ISBN (Electronic)978-3-9524-2698-2
ISBN (Print)978-1-5386-5303-6
Publication statusPublished - Jun 2018
Publication typeA4 Article in a conference publication
EventEuropean Control Conference -
Duration: 1 Jan 1900 → …


ConferenceEuropean Control Conference
Period1/01/00 → …


In this paper, we propose a new concept called Generalized Time Scaling (GTS) which as the name suggests is a generalization of the time scaling concept extensively used for the kino-dynamic motion planning of robots. Given a trajectory, a time scaling transformation modifies the motion profile of the trajectory while preserving the geometric path associated with it. In contrast, GTS transformation modifies both the motion profile as well as the geometric path of the given trajectory. We show that this feature of GTS can be leveraged to derive a new formulation for trajectory deformation which in turn has several key advantages over existing frameworks. Firstly, it directly works at the trajectory description level and does not require multiple reintegration of state space models. Secondly, it can can directly deform straight line and circular trajectories into complex shapes. Finally, the proposed formulation takes the form of an optimization problem which is interesting in itself and has potential beyond the proposed work. In particular, we use Augmented Lagrangian (AL) and Alternating Minimization (AM) to reformulate a complex non-convex problem into a sequence of distributed convex optimization problems. As an application, we use the trajectory deformation for the terminal heading correction, goal point correction, collision avoidance of non-holonomic mobile robots as well as for smoothing of trajectories consisting of piece-wise linear and circular segments.


  • collision avoidance, convex programming, geometry, mobile robots, piecewise linear techniques, trajectory control, trajectory deformation, geometric path, GTS transformation, generalized time scaling, augmented lagrangian, alternating minimization, non-convex problem, convex optimization problems, heading correction, goal point correction, non-holonomic mobile robots, piece-wise linear segments, circular segments, kino-dynamic motion planning, Trajectory, Strain, Robots, Optimization, Minimization, Collision avoidance, Acceleration

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