In this paper, we provide distance-aware error bounds for Kolmogorov Arnold Networks (KANs). We call our new error bounds estimator DAREK—Distance Aware Error for Kolmogorov networks. Z. Liu et al. [1] provide error bounds, which may be loose, lack distance-awareness, and are defined only up to an unknown constant of proportionality. We review the error bounds for Newton’s polynomial, which is then generalized to an arbitrary spline, under Lipschitz continuity assumptions. We then extend these bounds to nested compositions of splines, arriving at error bounds for KANs. We evaluate our method by estimating an object’s shape from sparse laser scan points. We use KAN to fit a smooth function to the scans and provide error bounds for the fit. We find that our method is faster than Monte Carlo approaches, and that our error bounds enclose the true obstacle shape reliably.

Learning from Demonstrations (LfD) via Behavior Cloning (BC) works well on multiple complex tasks. However, a limitation of the typical LfD approach is that it requires expert demonstrations for all scenarios, including those in which the algorithm is already well-trained. The recently proposed Learning from Interventions (LfI) overcomes this limitation by using an expert overseer. The expert overseer only intervenes when it suspects that an unsafe action is about to be taken. Although LfI significantly improves over LfD, the state-of-the-art LfI fails to account for delay caused by the expert's reaction time and only learns short-term behavior. We address these limitations by 1) interpolating the expert's interventions back in time, and 2) by splitting the policy into two hierarchical levels, one that generates sub-goals for the future and another that generates actions to reach those desired sub-goals. This sub-goal prediction forces the algorithm to learn long-term behavior while also being robust to the expert's reaction time. Our experiments show that LfI using sub-goals in a hierarchical policy framework trains faster and achieves better asymptotic performance than typical LfD.

This paper focuses on inverse reinforcement learning (IRL) to enable safe and efficient autonomous navigation in unknown partially observable environments. The objective is to infer a cost function that explains expert-demonstrated navigation behavior while relying only on the observations and state-control trajectory used by the expert. We develop a cost function representation composed of two parts: a probabilistic occupancy encoder, with recurrent dependence on the observation sequence, and a cost encoder, defined over the occupancy features. The representation parameters are optimized by differentiating the error between demonstrated controls and a control policy computed from the cost encoder. Such differentiation is typically computed by dynamic programming through the value function over the whole state space. We observe that this is inefficient in large partially observable environments because most states are unexplored. Instead, we rely on a closed-form subgradient of the cost-to-go obtained only over a subset of promising states via an efficient motion-planning algorithm such as A* or RRT. Our experiments show that our model exceeds the accuracy of baseline IRL algorithms in robot navigation tasks, while substantially improving the efficiency of training and test-time inference.

Various perceptual domains have underlying compositional semantics that are rarely captured in current models. We suspect this is because directly learning the compositional structure has evaded these models. Yet, the compositional structure of a given domain can be grounded in a separate domain thereby simplifying its learning. To that end, we propose a new approach to modeling bimodal perceptual domains that explicitly relates distinct projections across each modality and then jointly learns a bimodal sparse representation. The resulting model enables compositionality across these distinct projections and hence can generalize to unobserved percepts spanned by this compositional basis. For example, our model can be trained on red triangles and blue squares; yet, implicitly will also have learned red squares and blue triangles. The structure of the projections and hence the compositional basis is learned automatically; no assumption is made on the ordering of the compositional elements in either modality. Although our modeling paradigm is general, we explicitly focus on a tabletop building-blocks setting. To test our model, we have acquired a new bimodal dataset comprising images and spoken utterances of colored shapes (blocks) in the tabletop setting. Our experiments demonstrate the benefits of explicitly leveraging compositionality in both quantitative and human evaluation studies.

We present a physically interpretable, continuous threedimensional (3D) model for handling occlusions with applications to road scene understanding. We probabilistically assign each point in space to an object with a theoretical modeling of the reflection and transmission probabilities for the corresponding camera ray. Our modeling is unified in handling occlusions across a variety of scenarios, such as associating structure from motion (SFM) point tracks with potentially occluding objects or modeling object detection scores in applications such as 3D localization. For point track association, our model uniformly handles static and dynamic objects, which is an advantage over motion segmentation approaches traditionally used in multibody SFM. Detailed experiments on the KITTI raw dataset show the superiority of the proposed method over both state-of-the-art motion segmentation and a baseline that heuristically uses detection bounding boxes for resolving occlusions. We also demonstrate how our continuous occlusion model may be applied to the task of 3D localization in road scenes.

Various perceptual domains have underlying compositional semantics that are rarely captured in current models. We suspect this is because directly learning the compositional structure has evaded these models. Yet, the compositional structure of a given domain can be grounded in a separate domain thereby simplifying its learning. To that end, we propose a new approach to modeling bimodal percepts that explicitly relates distinct projections across each modality and then jointly learns a bimodal sparse representation. The resulting model enables compositionality across these distinct projections and hence can generalize to unobserved percepts spanned by this compositional basis. For example, our model can be trained on 'red triangles' and 'blue squares'; yet, implicitly will also have learned 'red squares' and 'blue triangles'. The structure of the projections and hence the compositional basis is learned automatically for a given language model. To test our model, we have acquired a new bimodal dataset comprising images and spoken utterances of colored shapes in a tabletop setup. Our experiments demonstrate the benefits of explicitly leveraging compositionality in both quantitative and human evaluation studies.

Using the inverse sensor model has been popular in occupancy grid mapping. However, it is widely known that applying the inverse sensor model to mapping requires certain assumptions that are not necessarily true. Even the works that use forward sensor models have relied on methods like expectation maximization or Gibbs sampling which have been succeeded by more effective methods of maximum a posteriori (MAP) inference over graphical models. In this paper, we propose the use of modern MAP inference methods along with the forward sensor model. Our implementation and experimental results demonstrate that these modern inference methods deliver more accurate maps more efficiently than previously used methods.

Concurrently estimating the 6-DOF pose of multiple cameras or robots - cooperative localization - is a core problem in contemporary robotics. Current works focus on a set of mutually observable world landmarks and often require inbuilt egomotion estimates; situations in which both assumptions are violated often arise, for example, robots with erroneous low quality odometry and IMU exploring an unknown environment. In contrast to these existing works in cooperative localization, we propose a cooperative localization method, which we call mutual localization, that uses reciprocal observations of camera-fiducials to obviate the need for egomotion estimates and mutually observable world landmarks. We formulate and solve an algebraic formulation for the pose of the two camera mutual localization setup under these assumptions. Our experiments demonstrate the capabilities of our proposal egomotion-free cooperative localization method: for example, the method achieves 2cm range and 0.7 degree accuracy at 2m sensing for 6-DOF pose. To demonstrate the applicability of the proposed work, we deploy our method on Turtlebots and we compare our results with ARToolKit [1] and Bundler [2], over which our method achieves a tenfold improvement in translation estimation accuracy.

Conversion of unorganized point clouds to surface reconstructions is increasingly required in the mobile robotics perception processing pipeline, particularly with the rapid adoption of RGB-D (color and depth) image sensors. Many contemporary methods stem from the work in the computer graphics community in order to handle the point clouds generated by tabletop scanners in a batch-like manner. The requirements for mobile robotics are different and include support for real-time processing, incremental update, localization, mapping, path planning, obstacle avoidance, ray-tracing, terrain traversability assessment, grasping/manipulation and visualization for effective human-robot interaction. We carry out a quantitative comparison of Greedy Projection and Marching cubes along with our voxel planes method. The execution speed, error, compression and visualization appearance of these are assessed. Our voxel planes approach first computes the PCA over the points inside a voxel, combining these PCA results across 2×2×2 voxel neighborhoods in a sliding window. Second, the smallest eigenvector and voxel centroid define a plane which is intersected with the voxel to reconstruct the surface patch (3-6 sided convex polygon) within that voxel. By nature of their construction these surface patches tessellate to produce a surface representation of the underlying points. In experiments on public datasets the voxel planes method is 3 times faster than marching cubes, offers 300 times better compression than Greedy Projection, 10 fold lower error than marching cubes whilst allowing incremental map updates.