Abstract: Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness, trustworthiness and plausibility, that are not easily achievable using standard approaches like genetic programming for symbolic regression. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. The algorithm uses a context-free grammar to produce models that are parameterized by a non-linear least squares local optimization procedure. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions.

Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on non-Euclidean domains like spheres, rotation groups, or spaces of positive-definite matrices. To do so, one must place a Gaussian process prior, or equivalently define a kernel, on the space of interest. Effective kernels typically reflect the geometry of the spaces they are defined on, but designing them is generally non-trivial. Recent work on the Riemannian Mat\'ern kernels, based on stochastic partial differential equations and spectral theory of the Laplace-Beltrami operator, offers promising avenues towards constructing such geometry-aware kernels. In this paper, we study techniques for implementing these kernels on manifolds of interest in robotics, demonstrate their performance on a set of artificial benchmark functions, and illustrate geometry-aware Bayesian optimization for a variety of robotic applications, covering orientation control, manipulability optimization, and motion planning, while showing its improved performance.

We consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an asynchronous model where only a random portion of nodes perform computation at each iteration, while the information exchange can be conducted between all the nodes and in an asymmetric fashion. For this setting, we propose an algorithm that combines gradient tracking with a network-level variance reduction (in contrast to variance reduction within each node). This enables each node to track the average of the gradients of the objective functions. Our theoretical analysis shows that the algorithm converges linearly, when the local objective functions are strongly convex, under mild connectivity conditions on the expected mixing matrices. In particular, our result does not require the mixing matrices to be doubly stochastic. In the experiments, we investigate a broadcast mechanism that transmits information from computing nodes to their neighbors, and confirm the linear convergence of our method on both synthetic and real-world datasets.

Online algorithms is a field that deals with algorithmic problems in which the input is not entirely known in advance, but rather arrives in a sequential way. The algorithm is required to make irrevocable decisions, only based on the input received at a given point, and to incur the corresponding irrevocable cost for each of them. Traditionally, in the analysis of online algorithms we assume, rather pessimistically, that an adversary always presents the algorithm with the worst case input. More precisely, the performance of online algorithms is evaluated by the competitive ratio [5], which is the worst-case ratio of total algorithm's cost to the cost of a computationally unlimited optimal algorithm that is aware of the entire request sequence in advance. On the other hand, one of the main goals in the field of machine learning is to predict the unknown based on data, and learn what the world looks like, rather than preparing for the worst that can happen. In an effort to exploit this, there has been a trend in recent years that tries to use machine learning predictions in order to deal with the inherent uncertainty in online algorithms, while still providing worst case performance guarantees. Specifically, one might think that directly using machine learning in online problems should enhance their performance, since by knowing, with some error, how the input looks like, we should be able to come up with almost optimal solutions/approximations. In reality, this turns out not to be true, since the error of the learner does not necessarily remain constant, and it could propagate during different phases of the algorithm and cause a much bigger error. In a recent work, Lykouris and Vassilvitski [4] tried to formulate a framework to provide formal guarantees for these learning augmented online algorithms, in terms of consistency and robustness.

The combination of LiDARs and cameras enables a mobile robot to perceive environments with multi-modal data, becoming a key factor in achieving robust perception. Traditional frame cameras are sensitive to changing illumination conditions, motivating us to introduce novel event cameras to make LiDAR-camera fusion more complete and robust. However, to jointly exploit these sensors, the challenging extrinsic calibration problem should be addressed. This paper proposes an automatic checkerboard-based approach to calibrate extrinsics between a LiDAR and a frame/event camera, where four contributions are presented. Firstly, we present an automatic feature extraction and checkerboard tracking method from LiDAR's point clouds. Secondly, we reconstruct realistic frame images from event streams, applying traditional corner detectors to event cameras. Thirdly, we propose an initialization-refinement procedure to estimate extrinsics using point-to-plane and point-to-line constraints in a coarse-to-fine manner. Fourthly, we introduce a unified and globally optimal solution to address two optimization problems in calibration. Our approach has been validated with extensive experiments on 19 simulated and real-world datasets and outperforms the state-of-the-art.

In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective functions. In other words, we focus on maximizing submodular functions that are defined as expectations over a class of submodular functions with an unknown distribution. We show that for monotone functions of this form, the stochastic continuous greedy algorithm attains an approximation ratio (in expectation) arbitrarily close to $(1-1/e) \approx 63\%$ using a polynomial estimation of the gradient. We argue that using this polynomial estimator instead of the prior art that uses sampling eliminates a source of randomness and experimentally reduces execution time.

While the majority of autonomous driving research has concentrated on everyday driving scenarios, further safety and performance improvements of autonomous vehicles require a focus on extreme driving conditions. In this context, autonomous racing is a new area of research that has been attracting considerable interest recently. Due to the fact that a vehicle is driven by its perception, planning, and control limits during racing, numerous research and development issues arise. This paper provides a comprehensive overview of the autonomous racing system built by team KAIST for the Indy Autonomous Challenge (IAC). Our autonomy stack consists primarily of a multi-modal perception module, a high-speed overtaking planner, a resilient control stack, and a system status manager. We present the details of all components of our autonomy solution, including algorithms, implementation, and unit test results. In addition, this paper outlines the design principles and the results of a systematical analysis. Even though our design principles are derived from the unique application domain of autonomous racing, they can also be applied to a variety of safety-critical, high-cost-of-failure robotics applications. The proposed system was integrated into a full-scale autonomous race car (Dallara AV-21) and field-tested extensively. As a result, team KAIST was one of three teams who qualified and participated in the official IAC race events without any accidents. Our proposed autonomous system successfully completed all missions, including overtaking at speeds of around $220 km/h$ in the IAC@CES2022, the world's first autonomous 1:1 head-to-head race.

With the ever growing number of space debris in orbit, the need to prevent further space population is becoming more and more apparent. Refueling, servicing, inspection and deorbiting of spacecraft are some example missions that require precise navigation and docking in space. Having multiple, collaborating robots handling these tasks can greatly increase the efficiency of the mission in terms of time and cost. This article will introduce a modern and efficient control architecture for satellites on collaborative docking missions. The proposed architecture uses a centralized scheme that combines state-of-the-art, ad-hoc implementations of algorithms and techniques to maximize robustness and flexibility. It is based on a Model Predictive Controller (MPC) for which efficient cost function and constraint sets are designed to ensure a safe and accurate docking. A simulation environment is also presented to validate and test the proposed control scheme.

Grammatical inference consists in learning a formal grammar as a finite state machine or as a set of rewrite rules. In this paper, we are concerned with inferring Nondeterministic Finite Automata (NFA) that must accept some words, and reject some other words from a given sample. This problem can naturally be modeled in SAT. The standard model being enormous, some models based on prefixes, suffixes, and hybrids were designed to generate smaller SAT instances. There is a very simple and obvious property that says: if there is an NFA of size k for a given sample, there is also an NFA of size k+1. We first strengthen this property by adding some characteristics to the NFA of size k+1. Hence, we can use this property to tighten the bounds of the size of the minimal NFA for a given sample. We then propose simplified and refined models for NFA of size k+1 that are smaller than the initial models for NFA of size k. We also propose a reduction algorithm to build an NFA of size k from a specific NFA of size k+1. Finally, we validate our proposition with some experimentation that shows the efficiency of our approach.

While significant research progress has been made in robot learning for control, unique challenges arise when simultaneously co-optimizing morphology. Existing work has typically been tailored for particular environments or representations. In order to more fully understand inherent design and performance tradeoffs and accelerate the development of new breeds of soft robots, a comprehensive virtual platform with well-established tasks, environments, and evaluation metrics is needed. In this work, we introduce SoftZoo, a soft robot co-design platform for locomotion in diverse environments. SoftZoo supports an extensive, naturally-inspired material set, including the ability to simulate environments such as flat ground, desert, wetland, clay, ice, snow, shallow water, and ocean. Further, it provides a variety of tasks relevant for soft robotics, including fast locomotion, agile turning, and path following, as well as differentiable design representations for morphology and control. Combined, these elements form a feature-rich platform for analysis and development of soft robot co-design algorithms. We benchmark prevalent representations and co-design algorithms, and shed light on 1) the interplay between environment, morphology, and behavior; 2) the importance of design space representations; 3) the ambiguity in muscle formation and controller synthesis; and 4) the value of differentiable physics. We envision that SoftZoo will serve as a standard platform and template an approach toward the development of novel representations and algorithms for co-designing soft robots' behavioral and morphological intelligence.