Up until now, Curiosity has been at the whim of its Earth-bound Nasa controllers who have decided the best route for it as it heads towards its primary mission destination of Mount Sharp.
On Tuesday all this changed when its autonomous navigation system took over, a move that should allow it to cover ground much quicker.
The 'autonav' system means Curiosity can analyse routes quicker than operators on the ground.
Mark Maimone, rover mobility engineer and rover driver at NASA's Jet Propulsion Laboratory in California, said: "Curiosity takes several sets of stereo pairs of images, and the rover's computer processes that information to map any geometric hazard or rough terrain.
"The rover considers all the paths it could take to get to the designated endpoint for the drive and chooses the best one."
The drive on Tuesday, the mission's 376th Martian day, or "sol," took Curiosity across a depression where ground-surface details had not been visible from the location where the previous drive ended.
Story continues after the slideshow...
This image taken by the Mast Camera on NASA's Curiosity rover highlights the geology of Mount Sharp, a mountain inside Gale Crater, where the rover landed.
Base Of Mount Sharp
South/Southwest Of Landing Site
This photo is from a test series of the 100-millimeter Mast Camera on NASA's Curiosity rover. It is looking south-southwest of the landing site and taken on Aug. 23, 2012.
More From Mast Cam
Another test photo from the Mast Camera on NASA's Curiosity Rover. Again, it's looking south-southwest on Aug. 23, 2012. The gravelly area of the landing site is visible in the foreground.
The landing site is visibile here in this portion of a 360-degree color panorama along the heights of Mount Sharp.
Big Wheels Rolling
This photo was taken by a front Hazard-Avoidance camera on NASA's Curiosity and shows track marks from the rover's first Martian drives.
Curiosity's Second Drive
Track marks are seen here after the NASA Curiosity rover completes a successful drive to an area of bedrock.
The donut-shaped tracks shown here make an infinity symbol, following the first two drives from NASA's curiosity rover. The drives took place on Aug. 22 and Aug. 27, respectively.
Heights Of Mount Sharp
The highest point of Mount Sharp visible from NASA's Curiosity rover is seen here in a high-resolution image taken on Aug. 18.
Traces Of The Landing
This mosaic image was created from images taken by the rover's Navigation cameras on Aug. 7 Pacific Time / Aug. 8 Eastern Time.
Curiosity's Extended Arm
This photo taken on Aug. 20 shows the many tools on Curiosity's extended arm.
NASA's Curiosity rover tests its wheels at its landing site on Aug. 21. Photo taken by the rover's Navigation cameras.
NASA's Curiosity rover fired its laser 50 times against these rocks at a mark called "Goulburn."
Rover Takes First 'Steps'
This overhead view shows NASA's Curiosity rover after its first successful test drive on Aug. 22, 2012.
Another Look At Rover's First Steps
Here's another view of the first track marks Rover left in the Martian surface on Aug. 22, 2012.
The drive included about 10 meters of autonomous navigation across hidden ground as part of a day's total drive of about 141 feet 43 meters.
Driver, John Wright, said: "We could see the area before the dip, and we told the rover where to drive on that part.
"We could see the ground on the other side, where we designated a point for the rover to end the drive, but Curiosity figured out for herself how to drive the uncharted part in between.
The latest drive brought the distance traveled since leaving Glenelg to 0.86 miles.
The remaining distance to the Mount Sharp entry point is about 4.46 miles along a "rapid transit route."