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Ensuring safe behavior for automated vehicles in unregulated traffic areas poses a complex challenge for the industry. It is an open problem to provide scalable and certifiable solutions to this challenge. We derive a trajectory planner based on model predictive control which interoperates with a monitoring system for pedestrian safety based on cellular automata. The combined planner-monitor system is demonstrated on the example of a narrow indoor parking environment. The system features deterministic behavior, mitigating the immanent risk of black boxes and offering full certifiability. By using fundamental and conservative prediction models of pedestrians the monitor is able to determine a safe drivable area in the partially occluded and unstructured parking environment. The information is fed to the trajectory planner which ensures the vehicle remains in the safe drivable area at any time through constrained optimization. We show how the approach enables solving plenty of situations in tight parking garage scenarios. Even though conservative prediction models are applied, evaluations indicate a performant system for the tested low-speed navigation.

Angular path integration is the ability of a system to estimate its own heading direction from potentially noisy angular velocity (or increment) observations. Non-probabilistic algorithms for angular path integration, which rely on a summation of these noisy increments, do not appropriately take into account the reliability of such observations, which is essential for appropriately weighing one's current heading direction estimate against incoming information. In a probabilistic setting, angular path integration can be formulated as a continuous-time nonlinear filtering problem (circular filtering) with observed state increments. The circular symmetry of heading direction makes this inference task inherently nonlinear, thereby precluding the use of popular inference algorithms such as Kalman filters and rendering the problem analytically inaccessible. Here, we derive an approximate solution to circular continuous-time filtering, which integrates state increment observations while maintaining a fixed representation through both state propagation and observational updates. Specifically, we extend the established projection-filtering method to account for observed state increments and apply this framework to the circular filtering problem. We further propose a generative model for continuous-time angular-valued direct observations of the hidden state, which we integrate seamlessly into the projection filter. Applying the resulting scheme to a model of probabilistic angular path integration, we derive an algorithm for circular filtering, which we term the circular Kalman filter. Importantly, this algorithm is analytically accessible, interpretable, and outperforms an alternative filter based on a Gaussian approximation.

We propose Generative Probabilistic Image Colorization, a diffusion-based generative process that trains a sequence of probabilistic models to reverse each step of noise corruption. Given a line-drawing image as input, our method suggests multiple candidate colorized images. Therefore, our method accounts for the ill-posed nature of the colorization problem. We conducted comprehensive experiments investigating the colorization of line-drawing images, report the influence of a score-based MCMC approach that corrects the marginal distribution of estimated samples, and further compare different combinations of models and the similarity of their generated images. Despite using only a relatively small training dataset, we experimentally develop a method to generate multiple diverse colorization candidates which avoids mode collapse and does not require any additional constraints, losses, or re-training with alternative training conditions. Our proposed approach performed well not only on color-conditional image generation tasks using biased initial values, but also on some practical image completion and inpainting tasks.

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on an Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.

Multi-fingered robotic grasping is an undeniable stepping stone to universal picking and dexterous manipulation. Yet, multi-fingered grippers remain challenging to control because of their rich nonsmooth contact dynamics or because of sensor noise. In this work, we aim to plan hand configurations by performing Bayesian posterior inference through the full stochastic forward simulation of the robot in its environment, hence robustly accounting for many of the uncertainties in the system. While previous methods either relied on simplified surrogates of the likelihood function or attempted to learn to directly predict maximum likelihood estimates, we bring a novel simulation-based approach for full Bayesian inference based on a deep neural network surrogate of the likelihood-to-evidence ratio. Hand configurations are found by directly optimizing through the resulting amortized and differentiable expression for the posterior. The geometry of the configuration space is accounted for by proposing a Riemannian manifold optimization procedure through the neural posterior. Simulation and physical benchmarks demonstrate the high success rate of the procedure.

This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy, under which the agent satisfies high-level complex tasks expressed as linear temporal logic (LTL) with desired satisfaction probability. In particular, the cost optimization of the trajectory that satisfies infinite-horizon tasks is considered, and the trade-off between reducing the expected mean cost and maximizing the probability of task satisfaction is analyzed. Instead of using traditional Rabin automata, the LTL formulas are converted to limit-deterministic B\"uchi automata (LDBA) with a more straightforward accepting condition and a more compact graph structure. The novelty of this work lies in the consideration of the cases that LTL specifications can be potentially infeasible and the development of a relaxed product MDP between PL-MDP and LDBA. The relaxed product MDP allows the agent to revise its motion plan whenever the task is not fully feasible and to quantify the violation measurement of the revised plan. A multi-objective optimization problem is then formulated to jointly consider the probability of the task satisfaction, the violation with respect to original task constraints, and the implementation cost of the policy execution, which is solved via coupled linear programs. To the best of our knowledge, it is the first work that bridges the gap between planning revision and optimal control synthesis of both plan prefix and plan suffix of the agent trajectory over the infinite horizon. Experimental results are provided to demonstrate the effectiveness of the proposed framework.

This work proposes a robotic pipeline for picking and constrained placement of objects without geometric shape priors. Compared to recent efforts developed for similar tasks, where every object was assumed to be novel, the proposed system recognizes previously manipulated objects and performs online model reconstruction and reuse. Over a lifelong manipulation process, the system keeps learning features of objects it has interacted with and updates their reconstructed models. Whenever an instance of a previously manipulated object reappears, the system aims to first recognize it and then register its previously reconstructed model given the current observation. This step greatly reduces object shape uncertainty allowing the system to even reason for parts of the objects that are currently not observable. This also results in better manipulation efficiency as it reduces the need for active perception of the target object during manipulation. To get a reusable reconstructed model, the proposed pipeline adopts i) TSDF for object representation, and ii) a variant of the standard particle filter algorithm for pose estimation and tracking of the partial object model. Furthermore, an effective way to construct and maintain a dataset of manipulated objects is presented. A sequence of real-world manipulation experiments is performed to show how future manipulation tasks become more effective and efficient by reusing reconstructed models of previously manipulated objects that were generated on the fly instead of treating objects as novel every time.

This paper introduces the equiwide clustering problem, where valid partitions must satisfy intra-cluster dissimilarity constraints. Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a predefined number of expected classes, but on a dissimilarity threshold. Its main goal is to ensure an upper bound on the error induced by ultimately replacing any object with its cluster representative. Under this constraint, we then primarily focus on minimizing the number of clusters, along with potential sub-objectives. We argue that equiwide clustering is a sound clustering problem, and discuss its relationship with other optimization problems, existing and novel implementations as well as approximation strategies. We review and evaluate suitable clustering algorithms to identify trade-offs between the various practical solutions for this clustering problem.

Robots operating in human environments need a variety of skills, like slow and fast walking, turning, and side-stepping. However, building robot controllers that can exhibit such a large range of behaviors is challenging, and unsolved. We present an approach that uses a model-based controller for imitating different animal gaits without requiring any real-world fine-tuning. Unlike previous works that learn one policy per motion, we present a unified controller which is capable of generating four different animal gaits on the A1 robot. Our framework includes a trajectory optimization procedure that improves the quality of real-world imitation. We demonstrate our results in simulation and on a real 12-DoF A1 quadruped robot. Our result shows that our approach can mimic four animal motions, and outperform baselines learned per motion.

We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and mathematical interpretation, and is able to express a wide variety of constraints such as resource limits and safety requirements. Density constraints can also avoid the time-consuming process of designing and tuning cost functions required by value function-based constraints to encode system specifications. We leverage the duality between density functions and Q functions to develop an effective algorithm to solve the density constrained RL problem optimally and the constrains are guaranteed to be satisfied. We prove that the proposed algorithm converges to a near-optimal solution with a bounded error even when the policy update is imperfect. We use a set of comprehensive experiments to demonstrate the advantages of our approach over state-of-the-art CRL methods, with a wide range of density constrained tasks as well as standard CRL benchmarks such as Safety-Gym.