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The transport performance of two feedback-coupled Brownian particles, which are subjected to the external force, the unbiased time-periodic force and thermal noise, is investigated in the double-well ratchet potential. The average velocity, the average diffusion coefficient and the Pe number are calculated, respectively. The results demonstrate that the transport characteristic of Brownian particles is different under the action of two factors of unbiased time-periodic force, amplitude and frequency. The former factor induces the increase of the average velocity and the average diffusion coefficient with the decrease of thermal noise intensity within certain limits, whereas the latter makes the average velocity decrease in the transport of coupled particles. Moreover, it is found there is an optimal value of the driving frequency at which the Pe number reaches its maximum. Remarkably, it is shown that the current reversal can be achieved by increasing the external force, and the directed transport can be enhanced by varying the structure of the ratchet potential and the intensity of noise.

For the Boltzmann equation with an external potential force depending only on the space variables, there is a family of stationary solutions, which are local Maxwellians with space dependent density, zero velocity and constant temperature. In this paper, we will study the nonlinear stability of these stationary solutions by using the energy method. The analysis combines the analytic techniques used for the conservation laws using the fluid-type system derived from the Boltzmann equation (cf. [14]) and the dissipative effects on the fluid and non-fluid components of the Boltzmann equation through the celebrated H-theorem. To our knowledge, this is the first result on the global classical solutions to the Boltzmann equation with external force and non-trivial large time behavior in the whole space.

Moving the torso laterally in a walking biped robot can be mechanically more torque-efficient than not moving the torso according to recent research. Motivated by this observation, a torque-efficient torso-moving balance control strategy of a walking biped robot subject to a persistent continuous external force is suggested and verified in this paper. The torso-moving balance control strategy consists of a preliminary step and two additional steps. The preliminary step (disturbance detection) is to perceive the application of an external force by a safety boundary of zero moment point, detected approximately from cheap pressure sensors. Step 1 utilizes center of gravity (COG) Jacobian, centroidal momentum matrix and linear quadratic problem calculation to shift the zero moment point to the center of the support polygon. Step 2 makes use of H_∞ controllers for a more stable state shift from single support phase to double support phase. By comparing the suggested torso moving control strategy to the original control strategy that we suggested previously, a mixed balance control strategy is suggested. The strategy is verified through numerical simulation results.

In this paper, we propose a force-resisting balance control strategy for a walking biped robot subject to an unknown continuous external force. We assume that the biped robot has 12 degrees of freedom (DOFs) with position-controlled joint motors, and that the unknown continuous external force is applied to the pelvis of the biped robot in the single support phase (SSP) walking gait. The suggested balance control strategy has three phases. Phase 1 is to recognize the application of an unknown external force using only zero moment point (ZMP) sensors. Phase 2 is to control the joint motors according to a method that uses a genetic algorithm and the linear interpolation technique. Against an external continuous force, the robot retrieves the pre-calculated solutions and executes the desired torques with interpolation performed in real time. Phase 3 is to make the biped robot move from the SSP to the double support phase (DSP), rejecting external disturbances using the sliding mode controller. The strategy is verified by numerical simulations and experiments.

External force observer for humanoid robots has been widely studied in the literature. However, most of the proposed approaches generally rely on information from six-axis force/torque sensors, which the small or medium-sized humanoid robots usually do not have. As a result, those approaches cannot be applied to this category of humanoid robots, which are widely used nowadays in education or research.

In this paper, we propose a Kalman filter-based observer to estimate the three components of an external force applied in any direction and at an arbitrary point of the robot’s structure. The observer is simple to implement and can easily run in real time using the embedded processor of a small or medium-sized humanoid robot such as Nao or Darwin-OP. Moreover, the observer does not require any changes to the robot’s hardware, as it only uses measurements from the available force-sensing resistors (FSR) inserted under the feet of the humanoid robot and from the robot’s inertial measurement unit (IMU).

The proposed observer was extensively validated on a Nao humanoid robot in both cases of standing still or walking while an external force was applied to the robot. In the conducted experiments, the observer successfully estimated the external force within a reasonable margin of error. Moreover, the experimental data and the MATLAB and C++/ROS implementations of the proposed observer are available as an open source package. https://goo.gl/VkhejY.