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This study proposes a novel method for the positioning and spatial orientation control of three inextensible segments of trunk-type robots. The suggested algorithm imposes a soft constraint assumption for the end-effector’s endpoint and a mandatory constraint on its direction. Simultaneously, the algorithm by-design enforces nonholonomic features on the robot segments in the form of arcs. An approximate robot spine curve is the key to the final robot state configuration based on the given conditions. The numeric simulation showed acceptable (less than 1 s) performance for single-core processing tasks. The parametric method finds the best proximate robot state solution and represents the gray box model in addition to existing learning or black-box inverse dynamics approaches. This study also shows that a multiple inverse kinematics answer constructs a single inverse dynamics solution that defines the robot actuators’ motion profiles, synchronized in time. Finally, this text presents rotational expressions and their outlines for controlling the manipulator’s tendons.