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How can I check whether the mobile robot is going correctly or not about the plan?

That is extremely use-case specific and we cannot possibly tell you. If your robot has successfully created a plan and the controller is successfully moving the robot, why would you expect that the robot wouldn't be "going correctly about the plan"?

Certainly, there's a variety of ways that navigation may be suboptimal and you may want to detect such events, but again, very use-case specific we cannot answer.