Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines
ACM Transactions on Graphics (TOG)
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Regular Article: Derivatives of the Matrix Exponential and Their Computation
Advances in Applied Mathematics
A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
Motion planning in virtual prototyping: practical considerations
ISATP '95 Proceedings of the 1995 IEEE International Symposium on Assembly and Task Planning
"-Quaternion Splines for the Smooth Interpolation of Orientations
IEEE Transactions on Visualization and Computer Graphics
Synthesizing animations of human manipulation tasks
ACM SIGGRAPH 2004 Papers
Interactive collision detection between deformable models using chromatic decomposition
ACM SIGGRAPH 2005 Papers
Interactive continuous collision detection for non-convex polyhedra
The Visual Computer: International Journal of Computer Graphics
Planning Algorithms
Fast continuous collision detection for articulated models
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
Creating High-quality Paths for Motion Planning
International Journal of Robotics Research
ScrewBender: Smoothing Piecewise Helical Motions
IEEE Computer Graphics and Applications
CHOMP: gradient optimization techniques for efficient motion planning
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
An analytical continuous-curvature path-smoothing algorithm
IEEE Transactions on Robotics
Sampling-based algorithms for optimal motion planning
International Journal of Robotics Research
Newton-Type Algorithms for Dynamics-Based Robot Movement Optimization
IEEE Transactions on Robotics
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We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by sample-based motion planners. Our approach uses cubic B-splines to generate trajectories that are C2 almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in environments with narrow passages. We also present a fast and reliable algorithm for collision checking between a robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in cluttered environments.