Parameterizing finger rolling and finger-object contacts in a differentiable manner is important for formulating dexterous manipulation as a trajectory optimization problem. In contrast to previous methods which often assume simplified geometries of the robot and object or do not explicitly model finger rolling, we propose a method to further extend the capabilities of dexterous manipulation by accounting for non-trivial geometries of both the robot and the object. By integrating the object's Signed Distance Field (SDF) with a sampling method, our method estimates contact and rolling-related variables in a differentiable manner and includes those in a trajectory optimization framework. This formulation naturally allows for the emergence of finger-rolling behaviors, enabling the robot to locally adjust the contact points. To evaluate our method, we introduce a benchmark featuring challenging multi-finger dexterous manipulation tasks, such as screwdriver turning and in-hand reorientation. Our method outperforms baselines in terms of achieving desired object configurations and avoiding dropping the object. We also successfully apply our method to a real-world screwdriver turning task and a cuboid alignment task, demonstrating its robustness to the sim2real gap.

Planning contact-rich interactions for multi-finger manipulation is challenging due to the high-dimensionality and hybrid nature of dynamics. Recent advances in data-driven methods have shown promise, but are sensitive to the quality of training data. Combining learning with classical methods like trajectory optimization and search adds additional structure to the problem and domain knowledge in the form of constraints, which can lead to outperforming the data on which models are trained. We present Diffusion-Informed Probabilistic Contact Search (DIPS), which uses an A* search to plan a sequence of contact modes informed by a diffusion model. We train the diffusion model on a dataset of demonstrations consisting of contact modes and trajectories generated by a trajectory optimizer given those modes. In addition, we use a particle filter-inspired method to reason about variability in diffusion sampling arising from model error, estimating likelihoods of trajectories using a learned discriminator. We show that our method outperforms ablations that do not reason about variability and can plan contact sequences that outperform those found in training data across multiple tasks. We evaluate on simulated tabletop card sliding and screwdriver turning tasks, as well as the screwdriver task in hardware to show that our combined learning and planning approach transfers to the real world.

Virtual Power Plants (VPPs) play a crucial role in the increasing grid and market integration of distributed energy resources. However, as VPP complexity and geographic scale increase, the variable nature of PV generation makes accurate prediction of the VPP aggregate output challenging. The problem is further exacerbated by the paucity of smart meter data, making some prosumers unobservable to the VPP aggregator. To address these challenges, we propose a Bayesian Vector Autoregression approach to quantify the generation variance of a VPP consisting of an aggregation of residential rooftop PV systems spread over a large geographical area. The key idea is to generate synthetic data for unobserved prosumers using observed prosumers’ local correlation microstructure and temporal cross-correlation, allowing the simulation of the VPP output. We demonstrate the efficacy of the proposed approach by using two different Australian data sets. We study two use cases, considering the impact of the level of prosumer observability and the VPP size on the variance of the aggregate VPP output. Compared to the existing approaches, the proposed nonparametric approach provides a more accurate forecast of VPP output variance, allowing the VPP operator to manage market risk better.

In this article, we present constrained Stein variational trajectory optimization (CSVTO), an algorithm for performing trajectory optimization with constraints on a set of trajectories in parallel. We frame constrained trajectory optimization as a novel form of constrained functional minimization over trajectory distributions, which avoids treating the constraints as a penalty in the objective and allows us to generate diverse sets of constraint-satisfying trajectories. Our method uses Stein variational gradient descent to find a set of particles that approximates a distribution over low-cost trajectories while obeying constraints. CSVTO is applicable to problems with differentiable equality and inequality constraints and includes a novel particle resampling step to escape local minima. By explicitly generating diverse sets of trajectories, CSVTO is better able to avoid poor local minima and is more robust to initialization. We demonstrate that CSVTO outperforms baselines in challenging highly constrained tasks, such as a 7-DoF wrench manipulation task, where CSVTO outperforms all baselines both in success and constraint satisfaction.

We propose a sample-based model predictive control (MPC) method for collision-free navigation that uses a normalizing flow as a sampling distribution, conditioned on the start, goal, environment, and cost parameters. This representation allows us to learn a distribution that accounts for both the dynamics of the robot and complex obstacle geometries. We propose a way to incorporate this sampling distribution into two sampling-based MPC methods, MPPI, and iCEM. However, when deploying these methods, the robot may encounter an out-of-distribution (OOD) environment. To generalize our method to OOD environments, we also present an approach that performs projection on the representation of the environment. This projection changes the environment representation to be more in-distribution while also optimizing trajectory quality in the true environment. Our simulation results on a 2-D double-integrator, a 12-DoF quadrotor and a seven-DoF kinematic manipulator suggest that using a learned sampling distribution with projection outperforms MPC baselines on both in-distribution and OOD environments over different cost functions, including OOD environments generated from real-world data.

—Trajectory optimization and optimal control are powerful tools for synthesizing complex robot behavior using appropriate cost functions and constraints. However, methods for solving the optimization problem are often prone to local minima and sensitive to initialization. Casting trajectory optimization as an inference problem can alleviate some of these issues by generating distributions over solutions. However, the resulting inference problem can be costly. In this work, we present an approach for using diffusion models to learn a distribution over constraint-satisfying low-cost trajectories. This learned distribution is then used as the initialization for an inference-based trajectory optimization algorithm. We exploit the composability of diffusion models to generalize the learned generative model to out-of-distribution constraints which consist of the composition of multiple in-distribution constraints. We demonstrate the benefit of our approach by showing improvement over baselines on a constrained 12DoF Quadrotor task and a 7DoF robot manipulator task.

We propose a Model Predictive Control (MPC) method for collision-free navigation that uses amortized variational inference to approximate the distribution of optimal control sequences by training a normalizing flow conditioned on the start, goal and environment. This representation allows us to learn a distribution that accounts for both the dynamics of the robot and complex obstacle geometries. We can then sample from this distribution to produce control sequences which are likely to be both goal-directed and collision-free as part of our proposed FlowMPPI sampling-based MPC method. However, when deploying this method, the robot may encounter an out-of-distribution (OOD) environment, i.e. one which is radically different from those used in training. In such cases, the learned flow cannot be trusted to produce low-cost control sequences. To generalize our method to OOD environments we also present an approach that performs projection on the representation of the environment as part of the MPC process. This projection changes the environment representation to be more in-distribution while also optimizing trajectory quality in the true environment. Our simulation results on a 2D double-integrator and a 3D 12DoF underactuated quadrotor suggest that FlowMPPI with projection outperforms state-of-the-art MPC baselines on both in-distribution and OOD environments, including OOD environments generated from real-world data.

When manipulating a novel object with complex dynamics, a state representation is not always available, for example, deformable objects. Learning both a representation and dynamics from observations requires large amounts of data. We propose Learned Visual Similarity Predictive Control (LVSPC), a novel method for data-efficient learning to control systems with complex dynamics and high-dimensional state spaces from images. LVSPC leverages a given simple model approximation from which image observations can be generated. We use these images to train a perception model that estimates the simple model state from observations of the complex system online. We then use data from the complex system to fit the parameters of the simple model and learn where this model is inaccurate, also online. Finally, we use Model Predictive Control and bias the controller away from regions where the simple model is inaccurate and thus where the controller is less reliable. We evaluate LVSPC on two tasks; manipulating a tethered mass and a rope. We find that our method performs comparably to state-of-the-art reinforcement learning methods with an order of magnitude less data. LVSPC also completes the rope manipulation task on a real robot with 80% success rate after only 10 trials, despite using a perception system trained only on images from simulation.

In this paper, we propose an MPC method for robot motion by formulating MPC as Bayesian Inference. We propose using amortized variational inference to approximate the posterior with a normalizing flow conditioned on the start, goal and environment. By using a normalizing flow to represent the posterior, we are able to model complex distributions. This is important for robotics, where real environments impose difficult constraints on trajectories. We also present an approach for generalizing the learned sampling distribution to novel environments outside the training distribution. We demonstrate that our approach generalizes to a difficult novel environment and outperform a baseline sampling-based MPC method on a navigation problem.

When the dynamics of a system are difficult to model and/or time-consuming to evaluate, such as in deformable object manipulation tasks, motion planning algorithms struggle to find feasible plans efficiently. Such problems are often reduced to state spaces where the dynamics are straightforward to model and evaluate. However, such reductions usually discard information about the system for the benefit of computational efficiency, leading to cases where the true and reduced dynamics disagree on the result of an action. This letter presents a formulation for planning in reduced state spaces that uses a classifier to bias the planner away from state-action pairs that are not reliably feasible under the true dynamics. We present a method to generate and label data to train such a classifier, as well as an application of our framework to rope manipulation, where we use a Virtual Elastic Band (VEB) approximation to the true dynamics. Our experiments with rope manipulation demonstrate that the classifier significantly improves the success rate of our RRT-based planner in several difficult scenarios which are designed to cause the VEB to produce incorrect predictions in key parts of the environment.

The uptake of behind-the-meter distributed energy resources in low-voltage distribution networks has progressed to a point where phenomena including overvoltage and reverse power flow are emerging. The limited nature of supervision and control on these networks require novel tools for operation and planning in this environment. In this paper, we propose a methodology for synthesizing stochastic demand and generation profiles for unobserved customers with rooftop PV, called prosumers. The proposed model bridges the gap between the limited available empirical data, and the large amount of high-quality, stochastic demand and generation data required for probabilistic analysis. The approach employs clustering analysis and a Dirichlet-categorical hierarchical model of the features of unobserved prosumers. Based on the data of clusters of prosumers, Markov chain models of demand and generation profiles are constructed from empirical data, and synthetic demand profiles are subsequently sampled from these. The sampled traces are cross-validated and show a good statistical fit to the observed data. Two case studies are considered to confirm the validity of the proposed methodology. The first studies the impact of behavioral differences on the synthetic demand profiles, while the second looks at the impact of varying solar generation penetration on demand profiles.

Battery storage, particularly residential battery storage coupled with rooftop photovoltaics (PV), is emerging as an essential component of the smart grid technology mix. However, including battery storage and other flexible resources like electric vehicles and loads with thermal inertia into a probabilistic analysis based on Monte Carlo (MC) simulation is challenging, because their operational profiles are determined by computationally intensive optimization. Additionally, MC analysis requires a large pool of statistically-representative demand profiles to sample from. As a result, the analysis of the network impact of PV-battery systems has attracted little attention in the existing literature. To fill these knowledge gaps, this paper proposes a novel probabilistic framework to study the impact of PV-battery systems on low-voltage distribution networks. Specifically, the framework incorporates home energy management (HEM) operational decisions within the MC time series power flow analysis. First, using available smart meter data, we use a Bayesian nonparametric model to generate statistically-representative synthetic demand and PV profiles. Second, a policy function approximation that emulates battery scheduling decisions is used to make the simulation of optimization-based HEM feasible within the MC framework. The efficacy of our method is demonstrated on three representative low-voltage feeders, where the computation time to execute our MC framework is 5% of that when using explicit optimization methods in each MC sample. The assessment results show that uncoordinated battery scheduling has a limited beneficial impact, which is against the conjecture that batteries will serendipitously mitigate the technical problems induced by PV generation.

Increasing installations of distributed electricity generation have vastly increased the need for stochastic generation and demand data. However, the effects of such installations is uncertain, as high quality data is not always available before an installation is completed. In particular, there is a need for stochastic models of demand and generation profiles for unobserved prosumers. The model formulated in this paper bridges the gap between the limited available empirical data, and the large amount of high-quality, stochastic demand and generation data required for network and system analysis. The approach employs clustering analysis and a Dirichlet-categorical hierarchical model of the features of unobserved prosumers. Based on the data of clusters of prosumers, Markov chain models of demand and generation profiles are constructed from empirical data, and synthetic demand profiles are subsequently sampled from these. The sampled traces are cross-validated and show a good statistical fit to the observed data, and then two case studies are considered. The first identifies distinct behavioural differences in demand for residential areas of differing population density. The second case study varies levels of solar generation penetration, and shows that it contributes to significant intra-day demand variance, but has little impact on evening peak demand.

The increasing uptake of residential batteries has led to suggestions that the prevalence of batteries on LV networks will serendipitously mitigate the technical problems induced by PV installations. However, in general, the effects of PV-battery systems on LV networks have not been well studied. Given this background, in this paper, we test the assertion that the uncoordinated operation of batteries improves network performance. In order to carry out this assessment, we develop a methodology for incorporating home energy management (HEM) operational decisions within a Monte Carlo (MC) power flow analysis comprising three parts. First, due to the unavailability of large number of load and PV traces required for MC analysis, we used a maximum a-posteriori Dirichlet process to generate statistically representative synthetic profiles. Second, a policy function approximation (PFA) that emulates the outputs of the HEM solver is implemented to provide battery scheduling policies for a pool of customers, making simulation of optimization-based HEM feasible within MC studies. Third, the resulting net loads are used in a MC power flow time series study. The efficacy of our method is shown on three typical LV feeders. Our assessment finds that uncoordinated PV-battery systems have little beneficial impact on LV networks.

This paper presents a framework for generating synthetic residential solar generation profiles. Using the Dirichlet process, characteristics can be clustered and assigned to unobservable connections in a network. This approach retains the variance of this assignment introduced by sparse data, and allows for profiles to be generated specific to individual characteristics. It is also demonstrated that a Markov process modelling changing solar irradiance can be defined from existing solar generation data, rather than specific solar irradiance data in the event that it is not available. This model was applied to data sourced from Ausgrid's Smart Grid, Smart City Program, and a limited initial application found that profiles specific to assigned characteristics could be generated successfully.