Contando cambios en la línea de tiempo con MySQL

SET @last_task = 0;
SELECT SUM(new_task) AS tasks_performed
FROM (
  SELECT 
    IF(@last_task = RobotShortestPath, 0, 1) AS new_task,
    @last_task := RobotShortestPath
  FROM table
  ORDER BY ??
) AS tmp

Actualizar para varias tablas
Desde una vista de normalización de la estructura de la base de datos, es mejor con una tabla y tener un archivo que identifique qué columna es qué robot, si eso no es posible por alguna razón, puede obtenerlo uniendo las tablas:

SET @last_task = 0;
SELECT robot_id, SUM(new_task) AS tasks_performed
FROM (
  SELECT 
    IF(@last_task = RobotShortestPath, 0, 1) AS new_task,
    @last_task := RobotShortestPath
  FROM (
    SELECT 1 AS robot_id, robot_log_1.* FROM robot_log_1
    UNION SELECT 2, robot_log_2.* FROM robot_log_2
    UNION SELECT 3, robot_log_3.* FROM robot_log_3
    UNION SELECT 4, robot_log_4.* FROM robot_log_4
    UNION SELECT 5, robot_log_5.* FROM robot_log_5
  ) as robot_log
  ORDER BY robot_id, robot_log_id
) AS robot_log_history
GROUP BY robot_id
ORDER BY tasks_performed DESC