Self-Supervised 3D Traversability Estimation with Proxy Bank Guidance

Traversability estimation is a crucial component in mobile robotics platforms for estimating where it should go. In the case of paved road conditions, the traversability estimation task can be regarded as a subset of road detection [5, 16] and semantic segmentation [17]. However, the human-supervised method is clearly limited in estimating traversability for unconstrained environments like off-road areas. According to the diversity of the road conditions, it is hard to determine the traversability of a mobile robot in advance by man-made predefined rules.

Self-supervised approaches [18, 19, 20, 13] are suggested in the robotics literature to estimate the traversability using proprioceptive sensors such as inertial measurement and force-torque sensors [13]. Since these tasks only measured traversability in the proprioceptive-sensor domain, they do not affect the robot’s future driving direction. To solve this problem, a study to predict terrain properties by combining image information with the robot’s self-supervision has been proposed [11]. They identify the terrain properties from haptic interaction and associate them with the image to facilitate self-supervised learning. This work demonstrates promising outputs for traversability estimation, but it does not take epistemic uncertainty into account that necessarily exists in the self-supervised data. Furthermore, image data-based learning approaches are still vulnerable to illumination changes that can reduce the performance of the algorithms. Therefore, range sensors such as 3D LiDAR can be a strong alternative [21].

To overcome such limitations, we propose self-supervised traversability estimation in unconstrained environments that can alleviate congenital uncertainty from 3D point cloud data.

One of the biggest challenges in learning with few labeled data is epistemic uncertainty. To handle this problem, researchers proposed deep metric learning (DML) [22], which learns embedding spaces and classifies an unseen sample in the learned space. Several works adopt the sampled mini-batches called episodes during training, which mimics the task with few labeled data to facilitate DML [23, 24, 25, 26]. These methods with episodic training strategies epitomize labeled data of each class as a single vector, referred to as a prototype [27, 28, 29, 30, 17]. The prototypes generated by these works require non-parametric procedures and insufficiently represent unlabeled data.

Other works [31, 32, 33, 34, 31, 35, 36] develop loss functions to learn an embedding space where similar examples are attracted, and dissimilar examples are repelled. Recently, proxy-based loss [37] is proposed. Proxies are representative vectors of the training data in the learned embedding spaces, which are obtained in a parametric way [38, 39]. Using proxies leads to better convergence as they reflect the entire distribution of the training data [37]. A majority of the works [38, 39] provides a single proxy for each class, whereas SoftTriple loss [40] adopts multiple proxies for each class. We adopt the SoftTriple loss, as traversable and non-traversable regions are represented as multiple clusters rather than a single one in the unstructured driving surfaces according to their complexity and roughness.

Our self-supervised framework aims to learn a mapping between point clouds to traversability. We call input data containing the traversability information as ‘query.’ The traversable regions are referred to as the ‘positive’ class, and the non-traversable regions are referred to as the ‘negative’ class in this work. In query data, only positive data are labeled along with their traversability. The rest remains as unlabeled regions. Non-black points in Fig. 2(a) indicate the positive regions and the black points indicate the unlabeled regions.

However, there exists a limitation in that the query data is devoid of any supervision about negative regions. With query data only, results would be unreliable, as negative regions can be regressed as a good traversable region due to the epistemic uncertainty (Fig. 1c.) Consequently, our task aims to learn semantic segmentation along with traversability regression to mask out the negative regions, thereby mitigating the epistemic uncertainty. Accordingly, we utilize a very small number of hand-labeled point cloud scenes and call it ‘support’ data. In support data, traversable and non-traversable regions are manually annotated as positive and negative, respectively. Manually labeling entire scenes can be biased with human intuitions. Therefore, only evident regions are labeled and used for training. Fig. 2(b) shows the example of labeled support data.

The overall schema of our task is illustrated in Fig. 3. When the input point cloud data is given, a segmentation mask is applied to the initial version of the traversability regression map, producing a masked traversability map as a final output. For training, we form an episode composed of queries and randomly sampled support data. We can optimize our network over both query and relatively small support data with the episodic strategy [17]. Also, to properly evaluate the proposed framework, we introduce a new metric that comprehensively measures the segmentation and the regression, while highlighting the nature of the traversability estimation task with the epistemic uncertainty.

Let query data, consisting of positive and unlabeled data, as ${Q}=\{{{Q}_{P}},{{Q}_{U}}\}$, and support data, consisting of positive and negative data, as ${S}=\{{{S}_{P}},{{S}_{N}}\}$. Let $P_{i}\in\mathbb{R}^{3}$ denotes the $3$D point, $a_{i}\in\mathbb{R}$ denotes the traversability, and $y_{i}\in\{0,1\}$ denotes the class of each point. Accordingly, data from ${Q}_{P}$, ${Q}_{U}$, ${S}_{P}$, and ${S}_{N}$ are in forms of $\{P_{i},a_{i},y_{i}\}$, $\{P_{i}\}$, $\{P_{i},y_{i}\}$, and $\{P_{i},y_{i}\}$, respectively. Let $f_{\theta}$ denote a feature encoding backbone where $\theta$ indicates a network parameter, $x_{i}\in\mathbb{R}^{d}$ as encoded features extracted from $P_{i}$, and $h_{\theta}$ as the multi-layer perceptron (MLP) head for the traversability regression. $g_{\theta}$ denotes the MLP head for the segmentation that distinguishes the traversable and non-traversable regions. The encoded feature domain for each data is notated as $\mathbb{Q}_{P}$, $\mathbb{Q}_{U}$, $\mathbb{S}_{P}$, and $\mathbb{S}_{N}$.

A baseline solution learns the network with labeled data only. ${Q}_{P}$ is used for the traversability regression and ${Q}_{P}$ and ${S}$ are both used for the segmentation. We obtain the traversability map $t_{i}=h(x_{i})$, $t_{i}\in\mathbb{R}$, and segmentation map $s_{i}=g(x_{i}),s_{i}\in\{0,1\}$. The final masked traversability map $T_{i}$ is represented as element-wise multiplication, $T_{i}=t_{i}\odot s_{i}$. The regression loss $L^{reg}$ is computed with $\mathbb{Q}_{p}$ and based on a mean squared error loss as Eq. (1), where $x_{i}$ is the $i$-th element of $\mathbb{Q}_{P}$.

For the segmentation loss $L^{seg}$, binary cross-entropy loss is used in the supervised setting as Eq. (2), where $x_{i}$ refers to the $i$-th element of either $\mathbb{Q}_{P}$ and $\mathbb{S}$. Both the positive query and the support data can be used for the segmentation loss as follows:

Combining the regression and the segmentation, the traversability estimation loss in the supervised setting is defined as follows:

Nonetheless, it does not fully take advantage of data captured under various driving surfaces. Since the learning is limited to the labeled data, it can not capture the whole characteristics of the training data. This drawback hinders the capability of the traversability estimation trained in a supervised manner.

We adopt metric learning to overcome the limitation of the fully-supervised solution. The objectives of metric learning are to learn embedding space and find the representations that epitomize the training data in the learned embedding space. To jointly optimize the embedding network and the representations, we adopt a proxy-based loss [39]. The embedding network is updated based on the positions of the proxies, and the proxies are adjusted by the updated embedding network iteratively. The proxies can be regarded as representations that abstract the training data. We refer this set of proxies as ‘proxy bank,’ denoted as $\mathbb{B}=\{\mathbb{B}_{P},\mathbb{B}_{N}\}$, where $\mathbb{B}_{P}$ and $\mathbb{B}_{N}$ indicate the set of proxies for each class. The segmentation map is inferred based on the similarity between feature vectors and the proxies of each class, as $s_{i}=g(\mathbb{B},x_{i})$.

The representations of traversable and non-traversable regions exhibit large intra-class variations, where numerous sub-classes exist in each class; flat ground or gravel road for positive, and rocks, trees, or bushes for negative. For the segmentation, we use SoftTriple loss [40] that utilizes multiple proxies for each class. The similarity between $x_{i}$ and class $c$, denoted as $S_{i,c}$, is defined by a weighted sum of cosine similarity between $x_{i}$ and $\mathbb{B}_{c}=$ {$p_{c}^{1},...,p_{c}^{K}$}, where $c$ denotes positive or negative, $K$ is the number of proxies per class, and $p_{c}^{k}$ is $k$-th proxy in the proxy bank. The weight given to each cosine similarity is proportionate to its value. $S_{i,c}$ is defined as follows:

where $T$ is a temperature parameter to control the softness of assignments. Soft assignments reduce sensitivity between multiple centers. Note that the $l_{2}$ norm has been applied to embedding vectors to sustain divergence of magnitude. Then the SoftTriple loss is defined as follows:

where $\lambda$ is a hyperparameter for smoothing effect and $\delta$ is a margin. The segmentation loss using the proxy bank can be reformulated using the SoftTriple loss as Eq. (6) and the traversability estimation loss using the proxy bank is defined as Eq. (7).

Unlabeled data, which is abundantly included in self-supervised traversability data, has not been considered in previous works. To enhance the supervision we can extract from the data, we utilize the unlabeled data in the query data in the learning process. The problem is that the segmentation loss cannot be applied to the $\mathbb{Q}_{U}$ because no class label $y_{i}$ exists for them. We assign an auxiliary target for each unlabeled data as clustering [41]. Pseudo class of $i$-th sample $\hat{y_{i}}$ is assigned based on the class of the nearest proxy in the embedding space as $\hat{y_{i}}=\operatorname*{argmax}_{c\in\{P,N\}}S_{i,c}$.

The unsupervised loss for the segmentation, denoted as $L^{U}$, is defined as Eq. (8) using the pseudo-class, where $x_{i}$ is an embedding of $i$-th sample in $\mathbb{Q}_{U}$.

Fig. 4 illustrates the benefit of incorporating unlabeled loss. The embedding network can learn to capture more broad distribution of data, and learned proxies would represent training data better. When unlabeled data features are assigned to the proxies (Fig. 4a,) the embedding space and proxies are updated as Fig. 4b, exhibiting more precise decision boundaries.

Combining the aforementioned objectives altogether, we define our final objective as ‘Traverse Loss,’ and is defined as Eq. (9). The overall high-level schema of the learning procedure is depicted in Fig. 5.

Our metric learning method can suffer from sub-optimal solutions, which are induced by empty proxies. Empty proxies indicate the proxies to which none of the data are assigned. Such empty proxies should be redeployed to be a good representation of training data. Otherwise, the model might lose the discriminative power and the bank might include semantically poor representations.

Our intuitive idea to circumvent an empty proxy is to re-initialize the empty proxy with support data features. By updating the empty proxies with support data, the proxy bank can reflect training data that was not effectively captured beforehand. In order to obtain representative feature vectors without noises, $M$ number of prototype feature vectors, denoted as $\mu^{+}=\{\mu_{m}^{+},m=1,...,M\}$ and $\mu^{-}=\{\mu_{m}^{-},m=1,...,M\}$, are estimated using an Expectation-Maximization algorithm [42]. The prototype vectors are cluster centers of support features. We randomly choose the prototype vectors with small perturbations and use them as re-initialized proxies. Algorithm 1 summarizes the overall training procedure of our method.

We devise a new metric for the proposed framework, ‘Traversability Precision Error’ (TPE). The new metric should be able to comprehensively evaluate the segmentation and the regression while taking the critical aspect of the traversability estimation into account. One of the most important aspects of traversability estimation is to avoid the false-positive of the traversable region, the region that is impossible to traverse but inferred as traversable. If such a region is estimated as traversable, a robot will likely go over that region, resulting in undesirable movements. The impact of the false-positive decreases if they are estimated as less traversable. TPE computes the degree of false-positive of the traversable region, extenuating its impact with the traversability $t_{i}$. The TPE is defined as Eq. (10) where $TN$, $FP$, and $FN$ denote the number of true negative, false positive, and false negative points of the traversable region, respectively.

We evaluate the performance of our method with TPE, the new criteria designed for the traversability estimation task, which evaluates segmentation and regression quality simultaneously. Additionally, we evaluate the segmentation quality with mean Interaction over Union [43] (mIoU). For each class, the IoU is calculated by $IoU=\frac{TP}{TP+FP+FN}$, where $TP$, $FP$, and $FN$ denote the number of true negatives, false positives, and false negative points of each class, respectively.