Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information

In this paper, we study fundamental limitations of disturbance attenuation of feedback systems, under the assumption that the controller has a finite horizon preview of the disturbance. In contrast with prior work, we extend Bode's integral equation for the case where the preview is made available to the controller via a general, finite capacity, communication system. Under asymptotic stationarity assumptions, our results show that the new fundamental limitation differs from Bode's only by a constant, which quantifies the information rate through the communication system. In the absence of asymptotic stationarity, we derive a universal lower bound which uses Shannon's entropy rate as a measure of performance. By means of a case-study, we show that our main bounds may be achieved

A Reactive and Efficient Walking Pattern Generator for Robust Bipedal Locomotion

Available possibilities to prevent a biped robot from falling down in the presence of severe disturbances are mainly Center of Pressure (CoP) modulation, step location and timing adjustment, and angular momentum regulation. In this paper, we aim at designing a walking pattern generator which employs an optimal combination of these tools to generate robust gaits. In this approach, first, the next step location and timing are decided consistent with the commanded walking velocity and based on the Divergent Component of Motion (DCM) measurement. This stage which is done by a very small-size Quadratic Program (QP) uses the Linear Inverted Pendulum Model (LIPM) dynamics to adapt the switching contact location and time. Then, consistent with the first stage, the LIPM with flywheel dynamics is used to regenerate the DCM and angular momentum trajectories at each control cycle. This is done by modulating the CoP and Centroidal Momentum Pivot (CMP) to realize a desired DCM at the end of current step. Simulation results show the merit of this reactive approach in generating robust and dynamically consistent walking patterns

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements

A Model Predictive approach for semi active suspension control problem of a full car

International audienceA suspension controller aims at enhancing the ride comfort and the handling of vehicle which are evaluated by the acceleration at center of gravity and the roll motion respectively. In this paper, a semi-active suspension Model Predictive Control (MPC) is designed for a full vehicle system equipped with 4 semi-active dampers. The main challenge in the semi-active suspension control problem is to tackle with the dissipativity constraints of the semi-active dampers, here recasted as input and state constraints. The controller is designed in the MPC framework where the effects of the unknown road disturbances are taken into account. An observer approach allows to estimate the road disturbance information to be used by the controller during the prediction step. Then, the MPC control law with road estimation (but without road preview) is computed by minimizing a quadratic cost function, giving a trade-off between the comfort and the handling, while guaranteeing some physical constraints of the semi-active dampers. Some simulation results performed on a nonlinear full car model are presented in order to illustrate the effectiveness of the proposed approach

Online Learning Robust Control of Nonlinear Dynamical Systems

In this work we address the problem of the online robust control of nonlinear dynamical systems perturbed by disturbance. We study the problem of attenuation of the total cost over a duration $T$ in response to the disturbances. We consider the setting where the cost function (at a particular time) is a general continuous function and adversarial, the disturbance is adversarial and bounded at any point of time. Our goal is to design a controller that can learn and adapt to achieve a certain level of attenuation. We analyse two cases (i) when the system is known and (ii) when the system is unknown. We measure the performance of the controller by the deviation of the controller's cost for a sequence of cost functions with respect to an attenuation $\gamma$, $R^p_t$. We propose an online controller and present guarantees for the metric $R^p_t$ when the maximum possible attenuation is given by $\overline{\gamma}$, which is a system constant. We show that when the controller has preview of the cost functions and the disturbances for a short duration of time and the system is known $R^p_T(\gamma) = O(1)$ when $\gamma \geq \gamma_c$, where $\gamma_c = \mathcal{O}(\overline{\gamma})$. We then show that when the system is unknown the proposed controller with a preview of the cost functions and the disturbances for a short horizon achieves $R^p_T(\gamma) = \mathcal{O}(N) + \mathcal{O}(1) + \mathcal{O}((T-N)g(N))$, when $\gamma \geq \gamma_c$, where $g(N)$ is the accuracy of a given nonlinear estimator and $N$ is the duration of the initial estimation period. We also characterize the lower bound on the required prediction horizon for these guarantees to hold in terms of the system constants

Gait generation via intrinsically stable MPC for a multi-mass humanoid model

We consider the problem of generating a gait with no a priori assigned footsteps while taking into account the contribution of the swinging leg to the total Zero Moment Point (ZMP). This is achieved by considering a multi-mass model of the humanoid and distinguishing between secondary masses with known pre-defined motion and the remaining, primary, masses. In the case of a single primary mass with constant height, it is possible to transform the original gait generation problem for the multi-mass system into a single LIP-like problem. We can then take full advantage of an intrinsically stable MPC framework to generate a gait that takes into account the swinging leg motion

ADV preview based nonlinear predictive control for maximizing power generation of a tidal turbine with hydrostatic transmission

As the development of tidal turbines attracts more and more attention in recent years, reliable design and efficient control of tidal turbines are becoming increasingly important. However, the majority of existing tidal turbines still utilize traditional fixed ratio geared transmissions and the associated control designs focus on simple feedback controllers that use measurements or possibly estimates of the turbine itself or current local tidal profile. Therefore, the measurement and control are inevitably affected by the inherent delay with respect to the current tidal speeds. This paper proposes a novel tidal turbine with continuously variable speed hydrostatic transmissions and a nonlinear predictive controller that uses short-term predictions of the approaching tidal speed field to enhance the maximum tidal power generations when the tidal speed is below the rated value. The controller is designed based on an offline finite-horizon continuous time minimization of a cost function, and an integral action is incorporated into the control loop to increase the robustness against parameter variations and uncertainties. A smooth second order sliding mode observer is also designed for parameter estimations in the control loop. A 150 kW tidal turbine with hydrostatic transmission is designed and implemented. The results demonstrate that the averaged generator power increases by 6.76% with this preview based nonlinear predictive controller compared with a classical non-predictive controller

Humanoid Momentum Estimation Using Sensed Contact Wrenches

This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.Comment: Submitted to the 15th IEEE RAS Humanoids Conference, to be held in Seoul, Korea on November 3 - 5, 201