A general solution to such problems has existed in one dimension since the 1960s (Meditch 1964), but not in three dimensions. Over the past decade, research has shown how to use modern mathematical optimization techniques to solve this problem for a Mars landing, with guarantees that the best solution can be found in time (Açikmeşe and Ploen 2007; Blackmore et al. 2010).

Because Earth’s atmosphere is 100 times as dense as that of Mars, aerodynamic forces become the primary concern rather than a disturbance so small that it can be neglected in the trajectory planning phase. As a result, Earth landing is a very different problem, but SpaceX and Blue Origin have shown that this too can be solved. SpaceX uses CVXGEN (Mattingley and Boyd 2012) to generate customized flight code, which enables very high-speed onboard convex optimization.

NEXT STEPS

Although high-precision landings from space have happened on Earth, challenges stand in the way of transferring this technology to landing on other bodies in the solar system.

One problem is navigation: precision landing requires that the rocket know precisely where it is and how fast it’s moving. While GPS is a great asset for Earth landing, everywhere else in the universe is a GPS-denied environment. Almost all planetary missions have relied on Earth-based navigation: enormous radio antennas track the vehicle, compute its position and velocity, and uplink that information to the vehicle’s flight computer. This is sufficient for landings that only need to be precise to many kilometers, but not for landings that need to be precise to many meters.

Analogous to driving while looking in the rearview mirror, Earth-based tracking gets less and less accurate at greater distances from the starting point. Instead, the focus needs to be on the destination planet in order to be able to land precisely on it. Deep Impact is an example of a mission that used its target to navigate (Henderson and Blume 2015), but (as its name implies) it was an impactor mission, not a landing.

Recent research has achieved navigation accuracy on the order of tens of meters (Johnson et al. 2015; Wolf et al. 2011) using terrain relative navigation, where the lander images the surface of the planet during landing and matches features with an onboard map to determine its location. This can be tested on Earth, at least in part, without the need to perform the entire reentry from space.

Several companies have used experimental vehicles, some of which are shown in Figure 6, to demonstrate powered descent technology with low-altitude hops. Using these vehicles, terrain relative navigation has been tested on Earth (Johnson et al. 2015), and a demonstration on Mars is being considered for the Mars 2020 rover mission. If this is successful, combining terrain relative naviga-