Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

Identification of Motion Controllers In Human Standing And Walking

The method of trajectory optimization with direct collocation has the potential to extract generalized and realistic motion controllers from long duration movement data without requiring extensive measurement equipment. Knowing motion controllers not only can improve clinic assessments on locomotor disabilities, but also can inspire the control of powered exoskeletons and prostheses for better performance. Three aims were included in this dissertation. Aim 1 was to apply and validate the trajectory optimization for identification of the postural controllers in standing balance. The trajectory optimization approach was first validated on the simulated standing balance data and demonstrated that it can extract the correct postural control parameters. Then, six types of postural feedback controllers, from simple linear to complex nonlinear, were identified on six young adults’ motion data that was collected in a standing balance experiment. Results indicated that nonlinear controllers with multiple time delay paths can best explain their balance motions. A stochastic trajectory optimization approach was proposed that can help finding practically stable controllers in the identification process. Aim 2 focused on the foot placement control in walking. Foot placement controllers were successfully identified through the trajectory optimization method on nine young adults’ perturbed walking motions. It was shown that a linear controller with pelvis position and velocity feedback, suggested by the linear inverted pendulum model, was not sufficient to explain their foot placement among multiple walking speeds. Nonlinear controllers or more feedback signals, such as pelvis acceleration, are needed. Foot placement control was applied on a powered leg exoskeleton to control its legs’ swing motion. Two healthy participants were able to achieve stable walking with the controlled exoskeleton. v Results suggested that the foot placement controller helped decelerate the swing motion at late swing. In Aim 3, the trajectory optimization method was used to identify joint impedance properties in walking. Results of the synthetic study showed that relatively close impedance parameters can be identified. Then, a preliminary study was done to identify the ankle joint impedance properties of two participants at two walking speeds. The identified impedance properties were close to previous studies and consistent between different participants and walking speeds

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller

Using Parameterized Black-Box Priors to Scale Up Model-Based Policy Search for Robotics

The most data-efficient algorithms for reinforcement learning in robotics are model-based policy search algorithms, which alternate between learning a dynamical model of the robot and optimizing a policy to maximize the expected return given the model and its uncertainties. Among the few proposed approaches, the recently introduced Black-DROPS algorithm exploits a black-box optimization algorithm to achieve both high data-efficiency and good computation times when several cores are used; nevertheless, like all model-based policy search approaches, Black-DROPS does not scale to high dimensional state/action spaces. In this paper, we introduce a new model learning procedure in Black-DROPS that leverages parameterized black-box priors to (1) scale up to high-dimensional systems, and (2) be robust to large inaccuracies of the prior information. We demonstrate the effectiveness of our approach with the "pendubot" swing-up task in simulation and with a physical hexapod robot (48D state space, 18D action space) that has to walk forward as fast as possible. The results show that our new algorithm is more data-efficient than previous model-based policy search algorithms (with and without priors) and that it can allow a physical 6-legged robot to learn new gaits in only 16 to 30 seconds of interaction time.Comment: Accepted at ICRA 2018; 8 pages, 4 figures, 2 algorithms, 1 table; Video at https://youtu.be/HFkZkhGGzTo ; Spotlight ICRA presentation at https://youtu.be/_MZYDhfWeL

Identification of the contribution of the ankle and hip joints to multi-segmental balance control

Background\ud \ud Human stance involves multiple segments, including the legs and trunk, and requires coordinated actions of both. A novel method was developed that reliably estimates the contribution of the left and right leg (i.e., the ankle and hip joints) to the balance control of individual subjects. \ud \ud Methods\ud \ud The method was evaluated using simulations of a double-inverted pendulum model and the applicability was demonstrated with an experiment with seven healthy and one Parkinsonian participant. Model simulations indicated that two perturbations are required to reliably estimate the dynamics of a double-inverted pendulum balance control system. In the experiment, two multisine perturbation signals were applied simultaneously. The balance control system dynamic behaviour of the participants was estimated by Frequency Response Functions (FRFs), which relate ankle and hip joint angles to joint torques, using a multivariate closed-loop system identification technique. \ud \ud Results\ud \ud In the model simulations, the FRFs were reliably estimated, also in the presence of realistic levels of noise. In the experiment, the participants responded consistently to the perturbations, indicated by low noise-to-signal ratios of the ankle angle (0.24), hip angle (0.28), ankle torque (0.07), and hip torque (0.33). The developed method could detect that the Parkinson patient controlled his balance asymmetrically, that is, the right ankle and hip joints produced more corrective torque. \ud \ud Conclusion\ud \ud The method allows for a reliable estimate of the multisegmental feedback mechanism that stabilizes stance, of individual participants and of separate leg

Genetically evolved dynamic control for quadruped walking

The aim of this dissertation is to show that dynamic control of quadruped locomotion is achievable through the use of genetically evolved central pattern generators. This strategy is tested both in simulation and on a walking robot. The design of the walker has been chosen to be statically unstable, so that during motion less than three supporting feet may be in contact with the ground. The control strategy adopted is capable of propelling the artificial walker at a forward locomotion speed of ~1.5 Km/h on rugged terrain and provides for stability of motion. The learning of walking, based on simulated genetic evolution, is carried out in simulation to speed up the process and reduce the amount of damage to the hardware of the walking robot. For this reason a general-purpose fast dynamic simulator has been developed, able to efficiently compute the forward dynamics of tree-like robotic mechanisms. An optimization process to select stable walking patterns is implemented through a purposely designed genetic algorithm, which implements stochastic mutation and cross-over operators. The algorithm has been tailored to address the high cost of evaluation of the optimization function, as well as the characteristics of the parameter space chosen to represent controllers. Experiments carried out on different conditions give clear indications on the potential of the approach adopted. A proof of concept is achieved, that stable dynamic walking can be obtained through a search process which identifies attractors in the dynamics of the motor-control system of an artificial walker

Humanoid gait generation via MPC: stability, robustness and extensions

Research on humanoid robots has made significant progress in recent years, and Model Predictive Control (MPC) has seen great applicability as a technique for gait generation. The main advantages of MPC are the possibility of enforcing constraints on state and inputs, and the constant replanning which grants a degree of robustness. This thesis describes a framework based on MPC for humanoid gait generation, and analyzes some theoretical aspects which have often been neglected. In particular, the stability of the controller is proved. Due to the presence of constraints, this requires proving recursive feasibility, i.e., that the algorithm is able to recursively guarantee that a solution satisfying the constraints is found. The scheme is referred to as Intrinsically Stable MPC (IS-MPC). A basic scheme is presented, and its stability and feasibility guarantees are discussed. Then, several extensions are introduced. The guarantees of the basic scheme are carried over to a robust version of IS-MPC. Furthermore, extension to uneven ground and to a more accurate multi-mass model are discussed. Experiments on two robotic platforms (the humanoid robots HRP-4 and NAO) are presented in the concluding section

Light-Weight Wearable Gyroscopic Actuators Can Modulate Balance Performance and Gait Characteristics:A Proof-of-Concept Study

Falling is a major cause of morbidity, and is often caused by a decrease in postural stability. A key component of postural stability is whole-body centroidal angular momentum, which can be influenced by control moment gyroscopes. In this proof-of-concept study, we explore the influence of our wearable robotic gyroscopic actuator “GyroPack” on the balance performance and gait characteristics of non-impaired individuals (seven female/eight male, 30 ± 7 years, 68.8 ± 8.4 kg). Participants performed a series of balance and walking tasks with and without wearing the GyroPack. The device displayed various control modes, which were hypothesised to positively, negatively, or neutrally impact postural control. When configured as a damper, the GyroPack increased mediolateral standing time and walking distance, on a balance beam, and decreased trunk angular velocity variability, while walking on a treadmill. When configured as a negative damper, both peak trunk angular rate and trunk angular velocity variability increased during treadmill walking. This exploratory study shows that gyroscopic actuators can influence balance and gait kinematics. Our results mirror the findings of our earlier studies; though, with more than 50% mass reduction of the device, practical and clinical applicability now appears within reach.</p

Whole-body control with disturbance rejection through a momentum-based observer for quadruped robots☆

This paper presents an estimator of external disturbances for legged robots, based on the system’s momentum. The estimator, along with a suitable motion planner for the trajectory of the robot’s center of mass and an optimization problem based on the modulation of ground reaction forces, devises a whole-body controller for the robot. The designed solution is tested on a quadruped robot within a dynamic simulation environment. The quadruped is stressed by external disturbances acting on stance and swing legs indifferently. The proposed approach is also evaluated through a comparison with two state-of-the-art solutions