This paper concerns the time-optimal control for objects described by a random differential inclusion with discontinous right-hand side, representing the second law of Newtonian mechanics and taking into account a complex model of resistance to motion. Such a task has broad technical applications, especially in robotics. By generalizing the concept of the classic switching curve to the switching region, it is possible to construct in practice a range of convenient suboptimal control structures that provide many advantages, especially in respect to robustness.

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