Online Binary Feature Learning for Loop Closure

Abstract: Loop closure is an essential module in long-term SLAM, as detecting and recognizing re-visited locations serves to bound localization drift and correct for geometric map distortions. It also provides a mechanism to recover from track loss. However, most methods employ offline learnt maps that cannot be customized to the feature space of new environments. This work explores a means to generate a loop closing map with online adaptive properties.

Motivation and Background

Loop closure is what I would call the the lost robot problem (in the vein of the kidnapped robot problem). No matter how much one wishes for a SLAM system to succeed, there are times when it just might fail. The local map process, if there is one, usually prevent track loss by maintaining a sense of location. This sense of location is achieved by recognizing and exploiting high-frequency or low time interval re-visits; imagine going to another room then back right away. Keeping a short term memory of recent observations to generate the data re-association will improve localization. However, if the re-visit spans a long enough distance or time, such that the memory component cannot succeed, then more global data re-association methods are needed; imagine going from home to work/school/grandma’s/etc. Welcome to loop closure.

Loop closure is a tricky problem to solve. Make a mistake and it is over for your map; unless you have a really good way of detecting mistakes during map re-optimization. Miss a re-visit and you stay lost; that’s certainly happened to me lots of times while driving! Robots just don’t have the corrective strategies humans have, so we roboticists have to balance the trade-off between detection and error rate. In our language, that’s called a precision-recall trade-off. As someone whose background is control and dynamical systems and whose lab likes to think in these terms, we thought it would benefit the loop-closure process if there were a way to incorporate motion insensitivity into the detection process (full credit goes to Guangcong for the initial idea during brainstorming sessions). Mathematically, the ideal outcome would be to have motion invariance, but theoeretically proving and then deriving an algorithm for this may or may not provide dividends per my colleague Stefano Soatto’s findings.^{1 2} Sometimes the answer leads to an efficient algorithm, sometimes the computational complexity is too high. More importantly, insensitivity is often much easier to implement in practice and has nice computational or numerical properties arising from the fact that insensitivity is like an approximate invariance (my words). In controls, we love insensitivity to nuisance signals. Unlike invariance, insensitivity can be dialed up or down. Furthermore, there is usually a computational relationship with insensitivity level, which means that both can be modulated together to identify the best operating point across these two factors. That idea fundamentally motivates and describes our SLAM research.

Learning Descriptors for Loop-Closure

The loop-closure solution builds from ideas found in the IBuiLD ³ loop closure implementation, as well as from empirically-adaptive descriptors like BOLD ⁴. Whereas BOLD aims for affine invariance of the binary descriptor by masking out bit coordinates sensitive to affine transformations, we mask out the ones that are sensitive across frames (i.e., temporal motion insensitivity). While BOLD is backed up by empirical evidence for its design, we focused on establishing core properties of the masked descriptors in order to confirm that the necessary topological properties of the masked Hamming space supported the data association needs of loop closure. In this case, that meant descriptor distances had the right properties and behaviors as binary coordinates were masked out. The final result led to a method with decent loop-closure performance.⁵ Though others have surpassed this, this technique had pretty strong performance at the time. We are currently working on a method that incorporates additional forms of insensitivity and a more efficient querying structure to arrive at an efficient, online method with very high precision at 100% recall for common benchmark loop closure data sets.