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To accomplish this you'll want to have your rospy.Subscriber callback simply save the latest message. Then use a rospy.Timer with a separate function that calls your processing code with the latest message on a fixed schedule.

class Node:
    ...
    self.subscriber = rospy.Subscriber(sub_topic, MessageType, self.sub_callback)
    self.publisher = rospy.Publisher(pub_topic, MessageType)
    rospy.Timer(rospy.Duration(1), self.timer_callback)

    def sub_callback(self, message):
        self.latest_message = message

    def timer_callback(self, _):
        self.processing_code(self.latest_message)

    def processing_code(self, message):
        ...
        self.publisher.pub(processed_message)