A method for monitoring a pet by a robot based on a grid map, comprising: Step 1: determining according to the grid map constructed by the robot, a present position point of the robot and a grid cell corresponding to the present position point of the robot, in the grid map; Step 2: determining a mutual position relationship between the pet and the robot based on wireless communication between a wireless signal device on the robot and a wireless signal device on the pet, and determining according to the mutual position relationship, a present position point of the pet and a grid cell corresponding to the present position point of the pet; Step 3: judging whether there is an obstacle cell or not in grid cells, in a preset range covered by a shooting angle of a camera of the robot, the shooting direction of the camera of the robot being the direction of the pet, and between the grid cell where the robot is located and the grid cell where the pet is located, when a judging result in Step 3 is NO, keeping a shooting direction of the camera of the robot facing to the pet and re-executing Step 2, and when the judging result in Step 3 is YES, entering Step 4; Step 4: determining a preset region taking the grid cell where the pet is located as a center point, determining passed cells as candidate monitoring cells one by one from short to long distance relationships between the passed cells in the preset region and the robot, judging whether there is an obstacle cell or not in a straight grid path between the considered candidate monitoring cell and the grid cell where the pet is located, when a judging result in Step 4 is NO, determining the candidate monitoring cell as a monitoring cell and entering Step 5, when the judging result in Step 4 is YES, judging whether a next passed cell is farthest from the robot or not, when a judging result is that the next passed cell is not farthest from the robot, re-executing Step 4, and when the judging result is that the next passed cell is farthest from the robot, directly determining the next passed cell as the monitoring cell and entering Step 5; and Step 5: controlling the robot to walk from the present position point to the monitoring cell to monitor the pet, wherein the obstacle cell is a corresponding grid cell where the robot detects an obstacle, and the passed cell is a grid cell that the robot has passed. Step 1: determining according to the grid map constructed by the robot, a present position point of the robot and a grid cell corresponding to the present position point of the robot, in the grid map; Step 2: determining a mutual position relationship between the pet and the robot based on wireless communication between a wireless signal device on the robot and a wireless signal device on the pet, and determining according to the mutual position relationship, a present position point of the pet and a grid cell corresponding to the present position point of the pet; Step 3: judging whether there is an obstacle cell or not in grid cells, in a preset range covered by a shooting angle of a camera of the robot, the shooting direction of the camera of the robot being the direction of the pet, and between the grid cell where the robot is located and the grid cell where the pet is located, when a judging result in Step 3 is NO, keeping a shooting direction of the camera of the robot facing to the pet and re-executing Step 2, and when the judging result in Step 3 is YES, entering Step 4; Step 4: determining a preset region taking the grid cell where the pet is located as a center point, determining passed cells as candidate monitoring cells one by one from short to long distance relationships between the passed cells in the preset region and the robot, judging whether there is an obstacle cell or not in a straight grid path between the considered candidate monitoring cell and the grid cell where the pet is located, when a judging result in Step 4 is NO, determining the candidate monitoring cell as a monitoring cell and entering Step 5, when the judging result in Step 4 is YES, judging whether a next passed cell is farthest from the robot or not, when a judging result is that the next passed cell is not farthest from the robot, re-executing Step 4, and when the judging result is that the next passed cell is farthest from the robot, directly determining the next passed cell as the monitoring cell and entering Step 5; and Step 5: controlling the robot to walk from the present position point to the monitoring cell to monitor the pet, wherein the obstacle cell is a corresponding grid cell where the robot detects an obstacle, and the passed cell is a grid cell that the robot has passed.