scholarly journals Trajectory Optimization On Manifolds with Applications to SO(3) and R3XS2

2018 ◽  
Author(s):  
Michael Watterson ◽  
Sikang Liu ◽  
Ke Sun ◽  
Trey Smith ◽  
Vijay Kumar
Keyword(s):  
Trajectory Optimization ◽  
Optimization On Manifolds

Trajectory optimization on manifolds with applications to quadrotor systems

2020 ◽  
Vol 39 (2-3) ◽  
pp. 303-320
Author(s):  
Michael Watterson ◽  
Sikang Liu ◽  
Ke Sun ◽  
Trey Smith ◽  
Vijay Kumar
Keyword(s):  
Riemannian Manifold ◽  
Lie Group ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Geometric Approach ◽  
Field Of View ◽  
Three Dimensions ◽  
Constrained Optimization Problem ◽  
Optimization On Manifolds ◽  
Almost All

Manifolds are used in almost all robotics applications even if they are not modeled explicitly. We propose a differential geometric approach for optimizing trajectories on a Riemannian manifold with obstacles. The optimization problem depends on a metric and collision function specific to a manifold. We then propose our safe corridor on manifolds (SCM) method of computationally optimizing trajectories for robotics applications via a constrained optimization problem. Our method does not need equality constraints, which eliminates the need to project back to a feasible manifold during optimization. We then demonstrate how this algorithm works on an example problem on [Formula: see text] and a perception-aware planning example for visual–inertially guided robots navigating in three dimensions. Formulating field of view constraints naturally results in modeling with the manifold [Formula: see text], which cannot be modeled as a Lie group. We also demonstrate the example of planning trajectories on [Formula: see text] for a formation of quadrotors within an obstacle filled environment.

Real-Time Onboard Trajectory Optimization Using Indirect Methods

2021 ◽  
Author(s):  
Sean M. Nolan ◽  
Clayton A. Smith ◽  
Jacob D. Wood
Keyword(s):  
Real Time ◽  
Trajectory Optimization ◽  
Indirect Methods
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