Is it possible to control movement of turtlesim by string msgs?

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Perhaps you can even do with only one node. In the same node, create a subscriber and a publisher. The subscriber, in its call back listens to string mesgs play/stop. Then, in a switch or if-else stmt, it publishes twist messages via publisher as explained above by Gerry.

I guess you can publish string "play"/"stop" via message std_msgs/String. Then you create another node listening to this topic. Based on the string received, this node publish topic 'cmd_vel' with message geometry_msgs/Twist. If the string is "play", then you set some linear/angular velocity in Twist message. This should be able to make it move. On the other side, if the string is "stop", just set linear/angular velocity as 0.

Hope this helps, Gerry