Vladimir Ivan

Traiko Dinev, Carlos Mastalli, Vladimir Ivan et al.

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.

Traiko Dinev, Wolfgang Merkt, Vladimir Ivan et al.

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.

Carlo Tiseo, Vladimir Ivan, Wolfgang Merkt et al.

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.

Ran Long, Christian Rauch, Tianwei Zhang et al.

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.

Henrique Ferrolho, Vladimir Ivan, Wolfgang Merkt et al.

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.

Wolfgang Merkt, Vladimir Ivan, Traiko Dinev et al.

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.

Traiko Dinev, Songyan Xin, Wolfgang Merkt et al.

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.

Henrique Ferrolho, Wolfgang Merkt, Vladimir Ivan et al.

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.

Yiming Yang, Vladimir Ivan, Wolfgang Merkt et al.

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.

Yiming Yang, Vladimir Ivan, Zhibin Li et al.

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.