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We first study the higher version of the relative topological complexity byusing the homotopic distance. We also introduced the generalized version of therelative topological complexity of a topological pair on both the Schwarz genusand the homotopic distance. With these concepts, we give some inequalitiesincluding the topological complexity and the Lusternik-Schnirelmann category,the most important parts of the study of robot motion planning in topology.Finally, by defining the parametrised topological complexity via the homotopicdistance, we present some estimates on the higher setting of this concept.

Different Types of Topological Complexity on Higher Homotopic Distance