Optimal control (OC) using inverse dynamics provides numerical benefits such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, to take advantage of these benefits in model predictive control (MPC) for legged robots, it is crucial to handle efficiently its large number of equality constraints. To accomplish this, we first (i) propose a novel approach to handle equality constraints based on nullspace parametrization. Our approach balances optimality, and both dynamics and equality-constraint feasibility appropriately, which increases the basin of attraction to high-quality local minima. To do so, we (ii) modify our feasibility-driven search by incorporating a merit function. Furthermore, we introduce (iii) a condensed formulation of inverse dynamics that considers arbitrary actuator models. We also propose (iv) a novel MPC based on inverse dynamics within a perceptive locomotion framework. Finally, we present (v) a theoretical comparison of optimal control with forward and inverse dynamics and evaluate both numerically. Our approach enables the first application of inverse-dynamics MPC on hardware, resulting in state-of-the-art dynamic climbing on the ANYmal robot. We benchmark it over a wide range of robotics problems and generate agile and complex maneuvers. We show the computational reduction of our nullspace resolution and condensed formulation (up to 47.3%). We provide evidence of the benefits of our approach by solving coarse optimization problems with a high convergence rate (up to 10 Hz of discretization). Our algorithm is publicly available inside CROCODDYL.

This work presents a novel RGB-D-inertial dynamic SLAM method that can enable accurate localisation when the majority of the camera view is occluded by multiple dynamic objects over a long period of time. Most dynamic SLAM approaches either remove dynamic objects as outliers when they account for a minor proportion of the visual input, or detect dynamic objects using semantic segmentation before camera tracking. Therefore, dynamic objects that cause large occlusions are difficult to detect without prior information. The remaining visual information from the static background is also not enough to support localisation when large occlusion lasts for a long period. To overcome these problems, our framework presents a robust visual-inertial bundle adjustment that simultaneously tracks camera, estimates cluster-wise dense segmentation of dynamic objects and maintains a static sparse map by combining dense and sparse features. The experiment results demonstrate that our method achieves promising localisation and object segmentation performance compared to other state-of-the-art methods in the scenario of long-term large occlusion.

This paper presents OpTaS, a task specification Python library for Trajectory Optimization (TO) and Model Predictive Control (MPC) in robotics. Both TO and MPC are increasingly receiving interest in optimal control and in particular handling dynamic environments. While a flurry of software libraries exists to handle such problems, they either provide interfaces that are limited to a specific problem formulation (e.g. TracIK, CHOMP), or are large and statically specify the problem in configuration files (e.g. EXOTica, eTaSL). OpTaS, on the other hand, allows a user to specify custom nonlinear constrained problem formulations in a single Python script allowing the controller parameters to be modified during execution. The library provides interface to several open source and commercial solvers (e.g. IPOPT, SNOPT, KNITRO, SciPy) to facilitate integration with established workflows in robotics. Further benefits of OpTaS are highlighted through a thorough comparison with common libraries. An additional key advantage of OpTaS is the ability to define optimal control tasks in the joint space, task space, or indeed simultaneously. The code for OpTaS is easily installed via pip, and the source code with examples can be found at https://github.com/cmower/optas.

Reliable contact simulation plays a key role in the development of (semi-)autonomous robots, especially when dealing with contact-rich manipulation scenarios, an active robotics research topic. Besides simulation, components such as sensing, perception, data collection, robot hardware control, human interfaces, etc. are all key enablers towards applying machine learning algorithms or model-based approaches in real world systems. However, there is a lack of software connecting reliable contact simulation with the larger robotics ecosystem (i.e. ROS, Orocos), for a more seamless application of novel approaches, found in the literature, to existing robotic hardware. In this paper, we present the ROS-PyBullet Interface, a framework that provides a bridge between the reliable contact/impact simulator PyBullet and the Robot Operating System (ROS). Furthermore, we provide additional utilities for facilitating Human-Robot Interaction (HRI) in the simulated environment. We also present several use-cases that highlight the capabilities and usefulness of our framework. Please check our video, source code, and examples included in the supplementary material. Our full code base is open source and can be found at https://github.com/cmower/ros_pybullet_interface.

Abstract--Planning and execution of agile locomotion maneuvers have been a longstanding challenge in legged robotics. It requires to derive motion plans and local feedback policies in real-time to handle the nonholonomy of the kinetic momenta. To achieve so, we propose a hybrid predictive controller that considers the robot's actuation limits and full-body dynamics. It combines the feedback policies with tactile information to locally predict future actions. Our predictive controller enables ANYmal robots to generate agile maneuvers in realistic scenarios. A crucial element is to track the local feedback policies as, in contrast to whole-body control, they achieve the desired angular momentum. To the best of our knowledge, our predictive controller is the first to handle actuation limits, generate agile locomotion maneuvers, and execute optimal feedback policies for low level torque control without the use of a separate whole-body controller. In the top clip, ANYmal jumped diagonally twice. In the middle clip, ANYmal jumped four times with a rotation of 30 degrees each. In the bottom clip, ANYmal jumped 15cm forward.

Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.

Optimal control is a widely used tool for synthesizing motions and controls for user-defined tasks under physical constraints. A common approach is to formulate it using direct multiple-shooting and then to use off-the-shelf nonlinear programming solvers that can easily handle arbitrary constraints on the controls and states. However, these methods are not fast enough for many robotics applications such as real-time humanoid motor control. Exploiting the sparse structure of optimal control problem, such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints. Despite that, DDP has been associated with poor numerical convergence, particularly when considering long time horizons. One of the main reasons is due to system instabilities and poor warm-starting (only controls). This paper presents control-limited Feasibility-driven DDP (Box-FDDP), a solver that incorporates a direct-indirect hybridization of the control-limited DDP algorithm. Concretely, the forward and backward passes handle feasibility and control limits. We showcase the impact and importance of our method on a set of challenging optimal control problems against the Box-DDP and squashing-function approach.

Safe and compliant control of dynamic systems in interaction with the environment, e.g., in shared workspaces, continues to represent a major challenge. Mismatches in the dynamic model of the robots, numerical singularities, and the intrinsic environmental unpredictability are all contributing factors. Online optimization of impedance controllers has recently shown great promise in addressing this challenge, however, their performance is not sufficiently robust to be deployed in challenging environments. This work proposes a compliant control method for redundant manipulators based on a superimposition of multiple passive task-space controllers in a hierarchy. Our control framework of passive controllers is inherently stable, numerically well-conditioned (as no matrix inversions are required), and computationally inexpensive (as no optimization is used). We leverage and introduce a novel stiffness profile for a recently proposed passive controller with smooth transitions between the divergence and convergence phases making it particularly suitable when multiple passive controllers are combined through superimposition. Our experimental results demonstrate that the proposed method achieves sub-centimeter tracking performance during demanding dynamic tasks with fast-changing references, while remaining safe to interact with and robust to singularities. he proposed framework achieves such results without knowledge of the robot dynamics and thanks to its passivity is intrinsically stable. The data further show that the robot can fully take advantage of the redundancy to maintain the primary task accuracy while compensating for unknown environmental interactions, which is not possible from current frameworks that require accurate contact information.

Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data. However, the intrinsic degeneracy of the Bayesian framework, as multiple combinations of elements can yield empirically indistinguishable results, prompts the question of model identifiability. We propose a novel framework for a systematic testing of the identifiability of a significant class of Bayesian observer models, with practical applications for improving experimental design. We examine the theoretical identifiability of the inferred internal representations in two case studies. First, we show which experimental designs work better to remove the underlying degeneracy in a time interval estimation task. Second, we find that the reconstructed representations in a speed perception task under a slow-speed prior are fairly robust.

We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding leads to a model free, non-parametric approach for calculation of an approximate solution to the control problem. This formulation admits a decomposition of the problem into an invariant and task dependent component. Consequently, we make much more efficient use of the sample data compared to previous sample based approaches in this domain, e.g., by allowing sample re-use across tasks. Numerical examples on test problems, which illustrate the sample efficiency, are provided.