arXiv subjects

Vladimir Ivan

Publications and source records attributed to Vladimir Ivan.

17 recordsLinked to original sources

arXiv2024

Online Multi-Contact Receding Horizon Planning via Value Function Approximation

Planning multi-contact motions in a receding horizon fashion requires a value function to guide the planning with respect to the future, e.g., building momentum to traverse large obstacles. Traditionally, the value function is approximated by computing trajectories in a prediction horizon (never executed) that foresees the future beyond the execution horizon. However, given the non-convex dynamics of multi-contact motions, this approach is computationally expensive. To enable online Receding Horizon Planning (RHP) of multi-contact motions, we find efficient approximations of the value function. Specifically, we propose a trajectory-based and a learning-based approach. In the former, namely RHP with Multiple Levels of Model Fidelity, we approximate the value function by computing the prediction horizon with a convex relaxed model. In the latter, namely Locally-Guided RHP, we learn an oracle to predict local objectives for locomotion tasks, and we use these local objectives to construct local value functions for guiding a short-horizon RHP. We evaluate both approaches in simulation by planning centroidal trajectories of a humanoid robot walking on moderate slopes, and on large slopes where the robot cannot maintain static balance. Our results show that locally-guided RHP achieves the best computation efficiency (95\%-98.6\% cycles converge online). This computation advantage enables us to demonstrate online receding horizon planning of our real-world humanoid robot Talos walking in dynamic environments that change on-the-fly.

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arXiv2023

RoLoMa: Robust Loco-Manipulation for Quadruped Robots with Arms

Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches tackle these issues reactively at the control stage. However, regardless of the controller, online motion execution can only be as robust as the system capabilities allow at any given state. This is why it is important to have good motion plans to begin with, where robustness is considered proactively. To this end, we propose a metric (derived from first principles) for representing robustness against external disturbances. We then use this metric within our trajectory optimization framework for solving complex loco-manipulation tasks. Through our experiments, we show that trajectories generated using our approach can resist a greater range of forces originating from any possible direction. By using our method, we can compute trajectories that solve tasks as effectively as before, with the added benefit of being able to counteract stronger disturbances in worst-case scenarios.

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arXiv2023

Topology-Based MPC for Automatic Footstep Placement and Contact Surface Selection

State-of-the-art approaches to footstep planning assume reduced-order dynamics when solving the combinatorial problem of selecting contact surfaces in real time. However, in exchange for computational efficiency, these approaches ignore joint torque limits and limb dynamics. In this work, we address these limitations by presenting a topology-based approach that enables model predictive control (MPC) to simultaneously plan full-body motions, torque commands, footstep placements, and contact surfaces in real time. To determine if a robot's foot is inside a contact surface, we borrow the winding number concept from topology. We then use this winding number and potential field to create a contact-surface penalty function. By using this penalty function, MPC can select a contact surface from all candidate surfaces in the vicinity and determine footstep placements within it. We demonstrate the benefits of our approach by showing the impact of considering full-body dynamics, which includes joint torque limits and limb dynamics, on the selection of footstep placements and contact surfaces. Furthermore, we validate the feasibility of deploying our topology-based approach in an MPC scheme and explore its potential capabilities through a series of experimental and simulation trials.

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arXiv2023

RGB-D-Inertial SLAM in Indoor Dynamic Environments with Long-term Large Occlusion

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.

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arXiv2022

RGB-D SLAM in Indoor Planar Environments with Multiple Large Dynamic Objects

This work presents a novel dense RGB-D SLAM approach for dynamic planar environments that enables simultaneous multi-object tracking, camera localisation and background reconstruction. Previous dynamic SLAM methods either rely on semantic segmentation to directly detect dynamic objects; or assume that dynamic objects occupy a smaller proportion of the camera view than the static background and can, therefore, be removed as outliers. Our approach, however, enables dense SLAM when the camera view is largely occluded by multiple dynamic objects with the aid of camera motion prior. The dynamic planar objects are separated by their different rigid motions and tracked independently. The remaining dynamic non-planar areas are removed as outliers and not mapped into the background. The evaluation demonstrates that our approach outperforms the state-of-the-art methods in terms of localisation, mapping, dynamic segmentation and object tracking. We also demonstrate its robustness to large drift in the camera motion prior.

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arXiv2022

Differentiable Optimal Control via Differential Dynamic Programming

Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use differentiable optimal control for which the gradients of the robot's motion with respect to the parameters are required. We propose a method to efficiently compute these gradients analytically via the differential dynamic programming (DDP) algorithm using sensitivity analysis (SA). We show that we must include second-order dynamics terms when computing the gradients. However, we do not need to include them when computing the motion. We validate our approach on the pendulum and double pendulum systems. Furthermore, we compare against using the derivatives of the iterative linear quadratic regulator (iLQR), which ignores these second-order terms everywhere, on a co-design task for the Kinova arm, where we optimize the link lengths of the robot for a target reaching task. We show that optimizing using iLQR gradients diverges as ignoring the second-order dynamics affects the computation of the derivatives. Instead, optimizing using DDP gradients converges to the same optimum for a range of initial designs allowing our formulation to scale to complex systems.

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arXiv2022

A Versatile Co-Design Approach For Dynamic Legged Robots

We present a versatile framework for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are typically based on random sampling or concurrent optimization. We propose a novel bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (i.e., the lower level). These motion-planning derivatives allow us to incorporate arbitrary design constraints and costs in an general-purpose nonlinear program (i.e., the upper level). Our approach allows for the use of any differentiable motion planner in the lower level and also allows for an upper level that captures arbitrary design constraints and costs. It efficiently optimizes the robot's morphology, payload distribution and actuator parameters while considering its full dynamics, joint limits and physical constraints such as friction cones. We demonstrate these capabilities by designing quadruped robots that jump and trot. We show that our method is able to design a more energy-efficient Solo robot for these tasks.

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arXiv2022

A Passive Navigation Planning Algorithm for Collision-free Control of Mobile Robots

Path planning and collision avoidance are challenging in complex and highly variable environments due to the limited horizon of events. In literature, there are multiple model- and learning-based approaches that require significant computational resources to be effectively deployed and they may have limited generality. We propose a planning algorithm based on a globally stable passive controller that can plan smooth trajectories using limited computational resources in challenging environmental conditions. The architecture combines the recently proposed fractal impedance controller with elastic bands and regions of finite time invariance. As the method is based on an impedance controller, it can also be used directly as a force/torque controller. We validated our method in simulation to analyse the ability of interactive navigation in challenging concave domains via the issuing of via-points, and its robustness to low bandwidth feedback. A swarm simulation using 11 agents validated the scalability of the proposed method. We have performed hardware experiments on a holonomic wheeled platform validating smoothness and robustness of interaction with dynamic agents (i.e., humans and robots). The computational complexity of the proposed local planner enables deployment with low-power micro-controllers lowering the energy consumption compared to other methods that rely upon numeric optimisation.

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arXiv2022

Sparse-Dense Motion Modelling and Tracking for Manipulation without Prior Object Models

This work presents an approach for modelling and tracking previously unseen objects for robotic grasping tasks. Using the motion of objects in a scene, our approach segments rigid entities from the scene and continuously tracks them to create a dense and sparse model of the object and the environment. While the dense tracking enables interaction with these models, the sparse tracking makes this robust against fast movements and allows to redetect already modelled objects. The evaluation on a dual-arm grasping task demonstrates that our approach 1) enables a robot to detect new objects online without a prior model and to grasp these objects using only a simple parameterisable geometric representation, and 2) is much more robust compared to the state of the art methods.

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arXiv2021

Memory Clustering using Persistent Homology for Multimodality- and Discontinuity-Sensitive Learning of Optimal Control Warm-starts

Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided with a poor initial guess. Recent work has focused on providing an initial guess from a learned model trained on samples generated during an offline exploration of the problem space. However, in practice the solutions contain discontinuities introduced by system dynamics or the environment. Additionally, in many cases multiple equally suitable, i.e., multi-modal, solutions exist to solve a problem. Classic learning approaches smooth across the boundary of these discontinuities and thus generalize poorly. In this work, we apply tools from algebraic topology to extract information on the underlying structure of the solution space. In particular, we introduce a method based on persistent homology to automatically cluster the dataset of precomputed solutions to obtain different candidate initial guesses. We then train a Mixture-of-Experts within each cluster to predict state and control trajectories to warm-start the optimal control solver and provide a comparison with modality-agnostic learning. We demonstrate our method on a cart-pole toy problem and a quadrotor avoiding obstacles, and show that clustering samples based on inherent structure improves the warm-start quality.

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arXiv2021

Sparsity-Inducing Optimal Control via Differential Dynamic Programming

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.

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arXiv2021

Inverse Dynamics vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization

Benchmarks of state-of-the-art rigid-body dynamics libraries report better performance solving the inverse dynamics problem than the forward alternative. Those benchmarks encouraged us to question whether that computational advantage would translate to direct transcription, where calculating rigid-body dynamics and their derivatives accounts for a significant share of computation time. In this work, we implement an optimization framework where both approaches for enforcing the system dynamics are available. We evaluate the performance of each approach for systems of varying complexity, for domains with rigid contacts. Our tests reveal that formulations using inverse dynamics converge faster, require less iterations, and are more robust to coarse problem discretization. These results indicate that inverse dynamics should be preferred to enforce the nonlinear system dynamics in simultaneous methods, such as direct transcription.

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arXiv2021

RigidFusion: Robot Localisation and Mapping in Environments with Large Dynamic Rigid Objects

This work presents a novel RGB-D SLAM approach to simultaneously segment, track and reconstruct the static background and large dynamic rigid objects that can occlude major portions of the camera view. Previous approaches treat dynamic parts of a scene as outliers and are thus limited to a small amount of changes in the scene, or rely on prior information for all objects in the scene to enable robust camera tracking. Here, we propose to treat all dynamic parts as one rigid body and simultaneously segment and track both static and dynamic components. We, therefore, enable simultaneous localisation and reconstruction of both the static background and rigid dynamic components in environments where dynamic objects cause large occlusion. We evaluate our approach on multiple challenging scenes with large dynamic occlusion. The evaluation demonstrates that our approach achieves better motion segmentation, localisation and mapping without requiring prior knowledge of the dynamic object's shape and appearance.

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arXiv2020

Optimizing Dynamic Trajectories for Robustness to Disturbances Using Polytopic Projections

This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem is not tractable for state-of-the-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator.

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arXiv2020

Modeling and Control of a Hybrid Wheeled Jumping Robot

In this paper, we study a wheeled robot with a prismatic extension joint. This allows the robot to build up momentum to perform jumps over obstacles and to swing up to the upright position after the loss of balance. We propose a template model for the class of such two-wheeled jumping robots. This model can be considered as the simplest wheeled-legged system. We provide an analytical derivation of the system dynamics which we use inside a model predictive controller (MPC). We study the behavior of the model and demonstrate highly dynamic motions such as swing-up and jumping. Furthermore, these motions are discovered through optimization from first principles. We evaluate the controller on a variety of tasks and uneven terrains in a simulator.

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arXiv2016

Scaling Sampling-based Motion Planning to Humanoid Robots

Planning balanced and collision-free motion for humanoid robots is non-trivial, especially when they are operated in complex environments, such as reaching targets behind obstacles or through narrow passages. We propose a method that allows us to apply existing sampling--based algorithms to plan trajectories for humanoids by utilizing a customized state space representation, biased sampling strategies, and a steering function based on a robust inverse kinematics solver. Our approach requires no prior offline computation, thus one can easily transfer the work to new robot platforms. We tested the proposed method solving practical reaching tasks on a 38 degrees-of-freedom humanoid robot, NASA Valkyrie, showing that our method is able to generate valid motion plans that can be executed on advanced full-size humanoid robots. We also present a benchmark between different motion planning algorithms evaluated on a variety of reaching motion problems. This allows us to find suitable algorithms for solving humanoid motion planning problems, and to identify the limitations of these algorithms.

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arXiv2016

iDRM: Humanoid Motion Planning with Real-Time End-Pose Selection in Complex Environments

In this paper, we propose a novel inverse Dynamic Reachability Map (iDRM) that allows a floating base system to find valid end-poses in complex and dynamically changing environments in real-time. End-pose planning for valid stance pose and collision-free configuration is an essential problem for humanoid applications, such as providing goal states for walking and motion planners. However, this is non-trivial in complex environments, where standing locations and reaching postures are restricted by obstacles. Our proposed iDRM customizes the robot-to-workspace occupation list and uses an online update algorithm to enable efficient reconstruction of the reachability map to guarantee that the selected end-poses are always collision-free. The iDRM was evaluated in a variety of reaching tasks using the 38 degree-of-freedom (DoF) humanoid robot Valkyrie. Our results show that the approach is capable of finding valid end-poses in a fraction of a second. Significantly, we also demonstrate that motion planning algorithms integrating our end-pose planning method are more efficient than those not utilizing this technique.

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