We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit a model that can simultaneously capture the topological information of the tether and the continuous location of the robot. In this work, we explicitly build a topological model of the configuration space of a tethered robot starting from a polygonal representation of the workspace where the robot moves. To do so, we first establish a link between the configuration space of the tethered robot and the universal covering space of the workspace, and then we exploit this link to develop an algorithm to compute a simplicial complex model of the configuration space. We show how this approach improves the performances of existing algorithms that build other types of representations of the configuration space. The proposed model can be computed in a fraction of the time required to build traditional homotopy-augmented graphs, and is continuous, allowing to solve the path planning task for tethered robots using a broad set of path planning algorithms.

Nonholonomic constraints restrict feasible velocities without reducing configuration-space dimension, which makes collision-free geometric paths generally non-executable for car-like robots. Ackermann steering further imposes curvature bounds and forbids in-place rotation, so escaping from narrow dead ends typically requires tightly sequenced forward and reverse maneuvers. Classical planners that decouple global search and local steering struggle in these settings because narrow passages occupy low-measure regions and nonholonomic reachability shrinks the set of valid connections, which degrades sampling efficiency and increases sensitivity to clearances. We study nonholonomic narrow dead-end escape for Ackermann vehicles and contribute three components. First, we construct a generator that samples multi-phase forward-reverse trajectories compatible with Ackermann kinematics and inflates their envelopes to synthesize families of narrow dead ends that are guaranteed to admit at least one feasible escape. Second, we construct a training environment that enforces kinematic constraints and train a policy using the soft actor-critic algorithm. Third, we evaluate against representative classical planners that combine global search with nonholonomic steering. Across parameterized dead-end families, the learned policy solves a larger fraction of instances, reduces maneuver count, and maintains comparable path length and planning time while under the same sensing and control limits. We provide our project as open source at https://github.com/gitagitty/cisDRL-RobotNav.git

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

Learning-based methods have shown promising performance for accelerating motion planning, but mostly in the setting of static environments.

We study GCS-TSP, a new variant of the Traveling Salesman Problem (TSP) defined over a Graph of Convex Sets (GCS) -- a powerful representation for trajectory planning that decomposes the configuration space into convex regions connected by a sparse graph. In this setting, edge costs are not fixed but depend on the specific trajectory selected through each convex region, making classical TSP methods inapplicable. We introduce GHOST, a hierarchical framework that optimally solves the GCS-TSP by combining combinatorial tour search with convex trajectory optimization. GHOST systematically explores tours on a complete graph induced by the GCS, using a novel abstract-path-unfolding algorithm to compute admissible lower bounds that guide best-first search at both the high level (over tours) and the low level (over feasible GCS paths realizing the tour). These bounds provide strong pruning power, enabling efficient search while avoiding unnecessary convex optimization calls. We prove that GHOST guarantees optimality and present a bounded-suboptimal variant for time-critical scenarios. Experiments show that GHOST is orders-of-magnitude faster than unified mixed-integer convex programming baselines for simple cases and uniquely handles complex trajectory planning problems involving high-order continuity constraints and an incomplete GCS.

This work was done when the author was with Rutgers University.

Abstract-- High degree-of-freedom dual-arm robots are becoming increasingly common due to their morphology enabling them to operate effectively in human environments. However, motion planning in real-time within unknown, changing environments remains a challenge for such robots due to the high dimensionality of the configuration space and the complex collision-avoidance constraints that must be obeyed. In this work, we propose a novel way to alleviate the curse of dimensionality by leveraging the structure imposed by shared joints (e.g. First, we build two dynamic roadmaps (DRM) for each kinematic chain (i.e. Then, we show that we can leverage this structure to efficiently search through the composition of the two roadmaps and largely sidestep the curse of dimensionality. Finally, we run several experiments in a real-world grocery store with this motion planner on a 19 DoF mobile manipulation robot executing a grocery fulfillment task, achieving 0.4s average planning times with 99.9% success rate across more than 2000 motion plans.