Capture Point Trajectories for Reduced Knee Bend using Step Time Optimization

Traditional force-controlled bipedal walking utilizes highly bent knees, resulting in high torques as well as inefficient, and unnatural motions. Even with advanced planning of center of mass height trajectories, significant amounts of knee-bend can be required due to arbitrarily chosen step timing. In this work, we present a method that examines the effects of adjusting the step timing to produce plans that only require a specified amount of knee bend to execute. We define a quadratic program that optimizes the step timings and is executed using a simple iterative feedback approach to account for higher order terms. We then illustrate the effectiveness of this algorithm by comparing the walking gait of the simulated Atlas humanoid with and without the algorithm, showing that the algorithm significantly reduces the required knee bend for execution. We aim to later use this approach to achieve natural, efficient walking motions on humanoid robot platforms

A generalization of Kantorovich operators for convex compact subsets

In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of probability Borel measures. By considering special cases of these parameters for particular convex compact subsets we obtain the classical Kantorovich operators defined in the one-dimensional and multidimensional setting together with several of their wide-ranging generalizations scattered in the literature. We investigate the approximation properties of these operators by also providing several estimates of the rate of convergence. Finally, the preservation of Lipschitz-continuity as well as of convexity are discussedComment: Research articl

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

Straight-Leg Walking Through Underconstrained Whole-Body Control

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.Comment: Submitted to 2018 IEEE International Conference on Robotics and Automatio

Model Pembelajaran Instruction, Doing, Dan Evaluating (Mpide) Dengan Video Kejadian Fisika Dalam Pembelajaran Fisika Di SMA

This research examines the “Model Pembelajaran Instruction, Doing, dan Evaluating (MPIDE)” with Physics Phenomenon Video in Physics Instruction at SMA. The research\u27s purpose are to determine the students activities, the effectiveness of model, and the students learning achievement retention. This research is a research action that implicated by one group pretest and posttest design for testing. This research conducted on SMA of Class XI with the techniques of data collection is the observation, interviews, and tests. Data analysis techniques are percentage, continuesly its described. The results of the students activities , the effectiveness of model, and the students learning achievement retention can improve each cycle. The average of the students activities from cycle one to cycle two is 69,17% to 73,33% with active activity category. The average of the effectiveness of model from cycle one to cycle two is 0.68 with anough effective category to 0.75 with effective category. The average of students learning achievement retention from cycle one to cycle two is 92.56% to 93.19% with high category. The research can be concluded that the model can improve the students activities, the effectiveness of model, and the students learning achievement retention when the model completed by dubbing on video

A Modification of Bernstein-Durrmeyer Operators with Jacobi Weights on the Unit Interval

The present paper is devoted to the study of a sequence of positive linear operators, acting on the space of all continuous functions on [0, 1] as well as on some weighted spaces of integrable functions on [0, 1]. These operators are, as a matter of fact, a generalization of the Bernstein-Durrmeyer operators with Jacobi weights. In particular, we present qualitative and approximation properties of these operators, also providing estimates of the rate of convergence. Moreover, by means of their asymptotic formula, we compare our operators with the Bernstein-Durrmeyer ones and a suitable modification of theirs, showing that, in suitable intervals, they provide a lower approximating error estimate

On the traction problem for steady elastic oscillations equations: the double layer potential ansatz

The three-dimensional traction problem for steady elastic oscillations equations is studied. Representability of its solution by means of a double layer potential is considered instead of the more usual simple layer potential

Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains

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On the Dirichlet problem for the Stokes system in multiply connected domains

The Dirichlet problem for the Stokes system in a multiply connected domain of R^n (n ≥ 2) is considered in the present paper. We give the necessary and sufficient conditions for the representability of the solution by means of a simple layer hydrodynamic potential, instead of the classical double layer hydrodynamic potential

On the double layer potential ansatz for the n-dimensional Helmholtz equation with Neumann condition

In the present paper we consider the Neumann problem for the ndimensional Helmholtz equation. In particular we deal with the problem of representability of the solutions by means of double layer potentials