Bio-mimetic Adaptive Force/Position Control Using Fractal Impedance

The ability of animals to interact with complex dynamics is unmatched in robots. Especially important to the interaction performances is the online adaptation of body dynamics, which can be modeled as an impedance behaviour. However, the variable impedance controller still possesses a challenge in the current control frameworks due to the difficulties of retaining stability when adapting the controller gains. The fractal impedance controller has been recently proposed to solve this issue. However, it still has limitations such as sudden jumps in force when it starts to converge to the desired position and the lack of a force feedback loop. In this manuscript, two improvements are made to the control framework to solve these limitations. The force discontinuity has been addressed introducing a modulation of the impedance via a virtual antagonist that modulates the output force. The force tracking has been modeled after the parallel force/position controller architecture. In contrast to traditional methods, the fractal impedance controller enables the implementation of a search algorithm on the force feedback to adapt its behaviour on the external environment instead of on relying on \textit{a priori} knowledge of the external dynamics. Preliminary simulation results presented in this paper show the feasibility of the proposed approach, and it allows to evaluate the trade-off that needs to be made when relying on the proposed controller for interaction. In conclusion, the proposed method mimics the behaviour of an agonist/antagonist system adapting to unknown external dynamics, and it may find application in computational neuroscience, haptics, and interaction control.

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.

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.

Safe and Compliant Control of Redundant Robots Using a Stack of Passive Task-Space Controllers

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 stack of multiple passive task-space controllers. 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 in a stack. Our experimental results demonstrate that the proposed method achieves sub-centimeter tracking performance during dynamic demanding tasks with fast-changing references, while remaining safe to interact with and robust to singularities. The proposed framework achieves this without knowledge of the robot dynamics and thanks to its passivity is intrinsically stable. The data further shows that the robot can fully take advantage of the null-space to maintain the primary task accuracy while compensating for external perturbations.

Optimisation of Body-ground Contact for Augmenting Whole-Body Loco-manipulation of Quadruped Robots

Legged robots have great potential to perform loco-manipulation tasks, yet it is challenging to keep the robot balanced while it interacts with the environment. In this paper we study the use of additional contact points for maximising the robustness of loco-manipulation motions. Specifically, body-ground contact is studied for enhancing robustness and manipulation capabilities of quadrupedal robots. We propose to equip the robot with prongs: small legs rigidly attached to the body which ensure body-ground contact occurs in controllable point-contacts. The effect of these prongs on robustness is quantified by computing the Smallest Unrejectable Force (SUF), a measure of robustness related to Feasible Wrench Polytopes. We apply the SUF to assess the robustness of the system, and propose an effective approximation of the SUF that can be computed at near-real-time speed. We design a hierarchical quadratic programming based whole-body controller that controls stable interaction when the prongs are in contact with the ground. This novel concept of using prongs and the resulting control framework are all implemented on hardware to validate the effectiveness of the increased robustness and newly enabled loco-manipulation tasks, such as obstacle clearance and manipulation of a large object.

Learning Whole-body Motor Skills for Humanoids

This paper presents a hierarchical framework for Deep Reinforcement Learning that acquires motor skills for a variety of push recovery and balancing behaviors, i.e., ankle, hip, foot tilting, and stepping strategies. The policy is trained in a physics simulator with realistic setting of robot model and low-level impedance control that are easy to transfer the learned skills to real robots. The advantage over traditional methods is the integration of high-level planner and feedback control all in one single coherent policy network, which is generic for learning versatile balancing and recovery motions against unknown perturbations at arbitrary locations (e.g., legs, torso). Furthermore, the proposed framework allows the policy to be learned quickly by many state-of-the-art learning algorithms. By comparing our learned results to studies of preprogrammed, special-purpose controllers in the literature, self-learned skills are comparable in terms of disturbance rejection but with additional advantages of producing a wide range of adaptive, versatile and robust behaviors.

Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. We have unified dynamics, costs, and constraints into a single concept -- action -- for greater efficiency and easy prototyping. Additionally, we propose a novel multiple-shooting method called Feasibility-prone Differential Dynamic Programming (FDDP). Our novel method shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms, and it has similar numerical behavior to state-of-the-art multiple-shooting methods. However, our method does not increase the computational complexity typically encountered by adding extra variables to describe the gaps in the dynamics. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multiple-shooting methods). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers for legged robots (e.g. jumping, front-flip) in the order of milliseconds.

Comparing Metrics for Robustness Against External Perturbations in Dynamic Trajectory Optimization

Dynamic trajectory optimization is a popular approach for generating optimal and dynamically consistent trajectories. In order to deal with model errors and perturbations, the trajectories are usually tracked with feedback controllers. Their robustness thus largely depends on the margins of stability and control authority the system retains. Manipulability ellipsoids and force polytopes are well-known tools for evaluating force and motion capabilities of robot manipulators. Increased control authority can be achieved by incorporating task constraints within those tools. However, they come with an increased computational cost. Additionally, their impact on resulting trajectory quality and control authority has not yet been benchmarked and compared. In this letter, we introduce a novel robustness metric, the residual force polytope, which takes the nominal torque required to maintain a posture into account. We further detail a benchmarking protocol including evaluation criteria and visualization tools to compare robustness metrics in dynamic trajectory optimization. To foster benchmarking and allow for reproducibility, we open source a flexible framework for dynamic trajectory optimization via direct transcription along with our benchmark protocols as supplementary materials. Finally, we include - to the best of our knowledge - the first holistic comparison between traditional energy minimization metrics, kinematic manipulability maximization, and force polytope methods.

Comparing Alternate Modes of Teleoperation for Constrained Tasks

Teleoperation of heavy machinery in industry often requires operators to be in close proximity to the plant and issue commands on a per-actuator level using joystick input devices. However, this is non-intuitive and makes achieving desired job properties a challenging task requiring operators to complete extensive and costly training. Despite this, operator fatigue is common with implications for personal safety, project timeliness, cost, and quality. While full automation is not yet achievable due to unpredictability and the dynamic nature of the environment and task, shared control paradigms allow operators to issue high-level commands in an intuitive, task-informed control space while having the robot optimize for achieving desired job properties. In this paper, we compare a number of modes of teleoperation, exploring both the number of dimensions of the control input as well as the most intuitive control spaces. Our experimental evaluations of the performance metrics were based on quantifying the difficulty of tasks based on the well known Fitts' law as well as a measure of how well constraints affecting the task performance were met. Our experiments show that higher performance is achieved when humans submit commands in low-dimensional task spaces as opposed to joint space manipulations.

Analytic Model for Quadruped Locomotion Task-Space Planning

Despite the extensive presence of the legged locomotion in animals, it is extremely challenging to be reproduced with robots. Legged locomotion is an dynamic task which benefits from a planning that takes advantage of the gravitational pull on the system. However, the computational cost of such optimization rapidly increases with the complexity of kinematic structures, rendering impossible real-time deployment in unstructured environments. This paper proposes a simplified method that can generate desired centre of mass and feet trajectory for quadrupeds. The model describes a quadruped as two bipeds connected via their centres of mass, and it is based on the extension of an algebraic bipedal model that uses the topology of the gravitational attractor to describe bipedal locomotion strategies. The results show that the model generates trajectories that agrees with previous studies. The model will be deployed in the future as seed solution for whole-body trajectory optimization in the attempt to reduce the computational cost and obtain real-time planning of complex action in challenging environments.