Control system for work vehicle, control method, and work vehicle

A control method for a work vehicle including a work implement, the method comprising:

• receiving actual topography information indicating an actual topography of a work target;
• determining a design surface positioned below the actual topography;
• generating a command signal to move the work implement along the design surface;
• determining if slip of the work vehicle has occurred;
• and
• raising the design surface when a blade tip of the work implement when the slip occurred is positioned below an initial target surface, the initial target surface being the design surface before the occurrence of the slip.

A work vehicle comprising:

• a work implement;
• and
• a controller configured to move the work implement along a design surface positioned blow an actual topography of a work target,
• the design surface being raised when a blade tip of the work implement when slip occurred with the work vehicle is positioned below an initial target surface, the initial target surface being the design surface before the occurrence of the slip.