A deterministic global optimization approach is proposed for theoptimal trajectory planning of D-joint industrial robots. After mappingCartesian knots into joint knots, by inverse kinematics, they areinterpolated with spline functions under constraints on jointaccelerations and jerks. An interval algorithm, a procedure based oninterval analysis techniques, is presented to determine an optimalpiecewise trajectory which globally minimizes the total travelling time.With arbitrarily sharp precision, this procedure solves the nonlinearlyconstrained optimization problem which is obtained using thebranch-and-bound principle where the branching is performed by uniformsubdivision and the bounding via interval inclusion functions. Theinterval algorithm, implemented in C++ with the PROFIL/BIAS libraries,has been applied to the optimal four-spline planning of a 6-joint arm,and computational results are included
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