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Necessary and sufficient LMI conditions for constraints satisfaction within a B-spline framework

This work presents a novel solution for the satisfaction of continuous-time constraints through the use of B-spline curves. Exploiting the B-splines functions properties (local support, convexity and positivity), we provide necessary and sufficient LMI (Linear Matrix Inequalities)-based conditions for the satisfaction of continuous-time constraints. We consider both inclusion and exclusion constraints (in relation with a predefined convex domain) and implement the latter as a MISDP (Mixed integer - Semi-definite Programming) problem. We highlight the approach for the motion planning issue of off-line trajectory generation with obstacle(s) avoidance guarantees.