Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots

2015 ◽  
Author(s):  
David C. Post ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Disturbance Rejection ◽  
Open Loop ◽  
Legged Robots ◽  
Periodic Motions ◽  
Biped Robots ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Control Authority ◽  
Flat Ground ◽  
Instantaneous Control

The locomotion of legged robots is inherently underactuated, which creates control challenges in terms of rejecting large disturbances. A detailed understanding of how the control authority of a robot evolves over a gait trajectory has the potential to inform the design of controllers that offer superior disturbance rejection capabilities without compromising the efficiency benefits that typically accompany underactuated legged robots. Previous work has shown how the system velocities of an underactuated mechanical system can be decomposed into directions aligned with the inputs, or controlled directions, and directions orthogonal to the inputs, or uncontrolled directions, and applied that decomposition to drive wheeled robots to rest. This decomposition fundamentally provides a measure of the instantaneous control authority of the robot. This paper examines how the same techniques can be applied to inform the control of biped robots walking with periodic gaits. This problem differs from those previously studied in that it necessarily involves ground impacts and non-zero desired velocities. A representative example of a two-link planar biped walking on flat ground shows how a simple open loop controller that implements heuristics identified through the velocity decomposition to make use of the available control authority can improve disturbance rejection when added to a hybrid zero dynamics-based controller.

Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

2018 ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Control Method ◽  
Basin Of Attraction ◽  
Energetic Efficiency ◽  
Underactuated Mechanical Systems ◽  
Cost Of Transport ◽  
Biped Robots ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Step Velocity ◽  
Walking Speeds

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree of freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by 1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, 2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and 3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the trends observed in 1) through 3) are consistent across different walking speeds.

scholarly journals Terrain-blind walking of planar underactuated bipeds via velocity decomposition-enhanced control

2019 ◽  
Vol 38 (10-11) ◽  
pp. 1307-1323 ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P Schmiedeler
Keyword(s):  
Feedback Control ◽  
Biped Robot ◽  
Rate Of Change ◽  
Energetic Cost ◽  
Practical Implementation ◽  
Leg Length ◽  
Cost Of Transport ◽  
Velocity Decomposition ◽  
Novel Approach ◽  
Hybrid Zero Dynamics

In this article, we develop and assess a novel approach for the control of underactuated planar bipeds that is based on velocity decomposition. The new controller employs heuristic rules that mimic the functionality of transverse linearization feedback control and that can be layered on top of a conventional hybrid zero dynamics (HZD)-based controller. The heuristics sought to retain HZD-based control’s simplicity and enhance disturbance rejection for practical implementation on realistic biped robots. The proposed control strategy implements a feedback on the time rate of change of the decomposed uncontrolled velocity and is compared with conventional HZD-based control and transverse linearization feedback control for both vanishing and non-vanishing disturbances. Simulation studies with a point-foot, three-link biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. For the non-vanishing case, the velocity decomposition-enhanced controller outperforms HZD-based control, but takes fewer steps on average before failure than transverse linearization feedback control when walking on uneven terrain without visual perception of the ground. The findings were validated experimentally on a planar, five-link biped robot for eight different uneven terrains. The velocity decomposition-enhanced controller outperformed HZD-based control while maintaining a relatively low specific energetic cost of transport (~0.45). The biped robot “blindly” traversed uneven terrains with changes in terrain height accumulating to 5% of its leg length using the stand-alone low-level controller.

scholarly journals Dynamics and stability of running on rough terrains

2019 ◽  
Vol 6 (3) ◽  
pp. 181729 ◽  
Author(s):  
Nihav Dhawale ◽  
Shreyas Mandre ◽  
Madhusudhan Venkadesan
Keyword(s):  
Sensory Feedback ◽  
Dimensionless Parameter ◽  
Sagittal Plane ◽  
Sensory Information ◽  
Open Loop ◽  
Rough Terrain ◽  
Two Dimensional ◽  
Flat Surfaces ◽  
And Control ◽  
Flat Ground

Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope also varies randomly. The orientational instability is significantly mitigated by minimizing the tangential collision, which typically requires sensory information and anticipatory strategies such as leg retraction. By analysing the propagation of perturbations, we derive a single dimensionless parameter that governs stability. This parameter provides guidelines for the design and control of both biological and robotic runners.

Foot Contact Interactions of a Clock Torqued Spring-Loaded Inverted Pendulum

2012 ◽  
Author(s):  
Steven Riddle ◽  
Justin Seipel
Keyword(s):  
Disturbance Rejection ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Robots ◽  
Contact Friction ◽  
Slip Model ◽  
Specific Interest ◽  
Mass System ◽  
Friction Models ◽  
Spring Loaded Inverted Pendulum

The clock-torqued spring-loaded inverted pendulum (CT-SLIP) model describes the robust dynamic stability properties observed in most animals and some legged robots. However, the model’s behavior is sensitive to changes in liftoff conditions such as those experienced on realistic terrain. Here the incorporation of friction at the foot-ground interface is explored on the CT-SLIP model with specific interest in improving the transient center-of-mass dynamics. Multiple friction models are presented and tuned to reflect a periodic center-of-mass gait. The transient dynamics with friction are analyzed in comparison to the CT-SLIP model and improvements to the settling time and disturbance rejection were found. This addition of foot-ground contact friction may allow for better understanding of center-of-mass system dynamics on realistic terrain.

Game Theoretic Modeling of a Steering Operation in a Haptic Shared Control Framework

2018 ◽  
Author(s):  
Amir H. Ghasemi
Keyword(s):  
Path Following ◽  
Open Loop ◽  
Shared Control ◽  
Automation System ◽  
Steering Control ◽  
Human Driver ◽  
Control Framework ◽  
Game Theoretic ◽  
Control Authority ◽  
Vehicle Trajectory

Haptic shared control is expected to achieve a smooth collaboration between humans and automated systems, because haptics facilitate mutual communication. This paper addresses a the interaction between the human driver and automation system in a haptic shared control framework using a non-cooperative model predictive game approach. In particular, we focused on a scenario in which both human and automation system detect an obstacle but select different paths for avoiding it. For such a scenario, the open-loop Nash steering control solution is derived and the influence of the human driver’s impedance and path following weights on the vehicle trajectory are investigated. It is shown that by modulating the impedance and the path following weight the control authority can be shifted between the human driver and the automation system.

A Disturbance Rejection Strategy for Asynchronous Motor of the Electric Vehicle in Speed-Open-Loop Operating Mode

2012 ◽  
Vol 479-481 ◽  
pp. 71-75 ◽  
Author(s):  
Gang Zheng ◽  
Jian Dong Wu ◽  
Ming Wei Kuang ◽  
Deng Zhang ◽  
Yang Yang
Keyword(s):  
Electric Vehicle ◽  
Disturbance Rejection ◽  
Control Method ◽  
Controller Design ◽  
Asynchronous Motor ◽  
Operating Mode ◽  
Open Loop ◽  
Parameter Uncertainties ◽  
Current Variation ◽  
On The Road

For any electric vehicle on the road, it is inevitable to be influenced by parameter uncertainties and some kinds of disturbance torques, which present challenge for the controller design in the electric vehicle. Therefore, control of the electric vehicle to achieve the safety running requirement becomes important. In this paper, we investigate the control method for electric drive system of the electric vehicle from both theoretical and applied perspectives, then, speed loop inverse based disturbance rejection control strategy is proposed. The proposed approach is illustrated by implementing it into an experimental platform. The experimental results demonstrated that the proposed control method can achieve rapid response to current variation at operating frequency of electric vehicle, and substantially suppress the adverse effect of current variation at high frequency.

Output feedback robust disturbance rejection tracking control design for a bipedal robotic system with articulation constraints

2021 ◽  
pp. 095965182093969
Author(s):  
Karla Rincón-Martínez ◽  
Alberto Luviano-Juárez ◽  
Clara L Santos-Cuevas ◽  
Isaac Chairez
Keyword(s):  
Disturbance Rejection ◽  
Controller Design ◽  
Tracking Error ◽  
Lyapunov Stability Theory ◽  
Biped Robot ◽  
Robotic System ◽  
Robot Dynamics ◽  
Numerical Representation ◽  
Biped Robots ◽  
Position Errors

The design of an output-based robust disturbance rejection controller, aimed to solve the state tracking for the articulations of an experimental biped robot, was the main outcome of this study. The robust disturbance rejection controller included an auxiliary hybrid observer entailed to recover the angular velocity for each articulation. The estimated states served to perform the approximation of disturbances and non-modeled parts in the biped robot dynamics by implementing an extended state observer structure. The observer used the tracking position errors as input information, as well as considering the limb articular constraints, which are natural for biologically inspired biped robots. The effect of state constraints motivated the implementation of a hybrid observer with saturated output error injection. The controller design used the estimation of constraint velocity for solving the design of a tracking trajectory control to resolve the reproduction of the gait cycle by the bipedal robotic system. The Lyapunov stability theory served to obtain the laws which adjust the observer gains as well as to prove the ultimate boundedness of the tracking error as well. The evaluation of the suggested controller was realized on a numerical representation of the biped robot. These simulations illustrated the tracking performance of the hybrid robust disturbance rejection controller for all biped robot articulations in a decentralized structure. Experimental evaluations were also considered to validate the robust disturbance rejection controller design. A fully actuated biped robot was constructed and controlled by the robust disturbance rejection controller. The tracking results obtained by the robust disturbance rejection controller (in both the numerical and experimental evaluations) overcame the classical approach performances of diverse controllers as state feedback (proportional-derivative form) and regular robust disturbance rejection controller which did not consider the articulation constraints.

Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Control Method ◽  
Basin Of Attraction ◽  
Time Derivative ◽  
Energetic Efficiency ◽  
Underactuated Mechanical Systems ◽  
Cost Of Transport ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Step Velocity ◽  
Walking Speeds

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree-of-freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the time derivative of the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by (1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, (2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and (3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the observed trends are consistent across different walking speeds.

Design of VRFT Based Feedback-feedforward Controllers for Enhancing Disturbance Rejection on Non-minimum Phase Systems

2020 ◽  
Vol 15 (2) ◽  
Author(s):  
Suresh Kumar Chiluka ◽  
A. Seshagiri Rao ◽  
Murali Mohan Seepana ◽  
G. Uday Bhaskar Babu
Keyword(s):  
Disturbance Rejection ◽  
Absolute Error ◽  
Open Loop ◽  
Minimum Phase ◽  
Performance Indices ◽  
Virtual Reference ◽  
Point Tracking ◽  
Controller Performance ◽  
Feedforward Controller ◽  
Phase Systems

AbstractIn this work, Virtual Reference Feedback Tuning (VRFT) based feedback-feedforward controllers are designed for non-minimum phase systems to enhance the disturbance rejection. In model based design methods the feedforward controller is inverse of the plant model reduces the controller performance in the presence of uncertainties. The novelty of the work lies in to design VRFT based controllers independently for the feedforward structure, which decouples set point tracking and disturbance rejection. The optimal filter selection and algorithms to design the controllers were proposed with non-measurable disturbance signal using open loop experimental data. These controllers are applied to discrete time non-minimum phase Flexible Transmission System (FTS) with no load, half load and full load conditions. The simulation study on FTS with feedback and feedback plus feedforward structures evaluates the effectiveness of proposed controllers. The performance indices like Integral Absolute Error (IAE), Integral Square Error (ISE), Total Variance (TV), VRFT Objective Function (JVR) and Fragility Index (FI) are used to compare the controller’s performance. The simulation results indicate that proposed feedback plus feedforward controller is superior to feedback controller.

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