Planning COM trajectory with variable height and foot position with reactive stepping for humanoid robots

Heerden, Kirill Van

doi:10.1109/icra.2015.7140080

Cited by 12 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The constraint (6) is linear with respect to the horizontal motion of the CoM (c x,y andc x,y ), but nonlinear with respect to its vertical motion (c z andc z ). Taking into account this nonlinear model in online computations is possible [1], but this requires more expensive computations, which would be better avoided with the limited CPU resources embedded in robots. As a result, various options have been proposed to circumvent this nonlinearity when generating walking motions online.…”

Section: Dynamic Feasibility Constraintsmentioning

confidence: 99%

“…A crucial part in biped walking motion generation is to ensure dynamic feasibility, which takes the form of a nonlinear constraint in the general case. While it is possible to account for this nonlinear constraint in online computations [1], [2], this requires expensive computations which would be better avoided with the limited CPU resources embedded in robots. As a result, various options have been proposed to circumvent this nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A robust linear MPC approach to online generation of 3D biped walking motion

Brasseur

Sherikov

Collette

et al. 2015

2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids)

View full text Add to dashboard Cite

International audienceA crucial part in biped walking motion generation is to ensure dynamic feasibility, which takes the form of a nonlinear constraint in the general case. Our proposition is to bound the nonlinear part of the dynamic feasibility constraint between some properly chosen extreme values. Making sure that this constraint is satisfied for the extreme values guarantees its satisfaction for all possible values in between. This follows a classical approach from robust nonlinear control theory, which is to consider a nonlinear dynamical system as a specific selection of a time-invariant Linear Differential Inclusion. As a result, dynamic feasibility can be imposed by using only linear constraints, which can be included in an efficient linear MPC scheme, to generate 3D walking motions online. Our simulation results show two major achievements: 1) walking motions over uneven ground such as stairs can be generated online, with guaranteed kinematic and dynamic feasibility, 2) walking on flat ground is significantly improved, with a 3D motion of the CoM closely resembling the one observed in humans

show abstract

Section: Dynamic Feasibility Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A robust linear MPC approach to online generation of 3D biped walking motion

Brasseur

Sherikov

Collette

et al. 2015

2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids)

View full text Add to dashboard Cite

show abstract

“…1a and it is an extension of the authors previous work [5]. This paper further enhances that work by providing experimental verification, theoretically analyzing velocity disturbances rejection capacity with variable COM height.…”

Section: Introductionmentioning

confidence: 56%

“…Where P k flr,i (j) , p k flr,i (j) and σ k flr,i (j) parameterize a quadratic that constraints the vertical foot positions to the approximate floor shape around the vicinity of the robot at time k. This may not be sufficient to adequately describe the floor shape, in this case it is possible to parameterize the floor shape with a general nonlinear function and solve the resulting Nonlinear Programing Problem (NLP) with SQP, this approach has greater flexibility but is also computationally more expensive, see the authors earlier work for a simulation of such an approach [5].…”

Section: ) Goal Functionmentioning

confidence: 98%

Real-Time Variable Center of Mass Height Trajectory Planning for Humanoids Robots

Heerden

2017

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

This paper presents a trajectory planner for humanoid robots based on nonlinear model predictive control that can generate trajectories with variable center of mass heights and adaptive foot positions in real-time. This is done by analytically formulating the zero moment point constraint as a quadratic function that includes the vertical center of mass state. This constraint is then combined with linear foot position constraints, constraints on the vertical center of mass state and a quadratic goal function to form a quadratically constrained quadratic program. This program is then solved via sequential quadratic programing. It can be solved in less than 5 ms on average with a 3.4 Ghz CPU by taking advantage of the fact that the analytic problem formulation allows the analytical gradients to be computed, thus time consuming numerical differentiation is avoided and the gradient computation time is reduced from 12.4 ms to 0.12 ms. An experiment on a 3.5 Kg robot is conducted to verify the effectiveness of this algorithm in walking on a terrain where the two feet are at different heights. Lastly it is shown via simulation that the proposed approach can improve disturbance recovery capacity by up to 7%.

show abstract

“…Considering the nonlinear ZMP constraint, a way to generate 3D CoM motion is presented in [14] in which the ZMP constraint is expressed in quadratic form and then the problem can be solved as a quadratically constrained quadratic program. In order to handle the height variations on rough terrain, Feng et al [15] generated 3D CoM trajectory using Differential Dynamic Programming with explicitly added vertical component to their CoM model.…”

Section: Introductionmentioning

confidence: 99%

Straight leg walking strategy for torque-controlled humanoid robots

You

Xin

Zhou

et al. 2016

2016 IEEE International Conference on Robotics and Biomimetics (ROBIO)

View full text Add to dashboard Cite

Most humanoid robots walk in an unhuman-like way with bent knees due to the use of the simplified Linear Inverted Pendulum Model (LIPM) which constrains the Center of Mass (CoM) in a horizontal plane. Therefore it results in high knee joint torque and extra energy consumption. To address this issue, we propose a simple yet efficient c ontrol s trategy to realize straight leg walking. First, theoretical analyses of simplified m odels p rovide i nsight i nto Z ero M oment P oint (ZMP) deviations during straight knee walking. Based on the finding that the deviation is limited comparing to the support polygon, we decide to keep using the LIPM for high-level planning, but let the robot perform straight leg walking automatically via the optimization-based low-level controller. By setting the desired CoM height slightly over the robot's reachable height, the lowlevel controller will attempt to straighten the robot's leg to reach this vertical reference, in the meanwhile, also satisfy the constraints (i.e. dynamic feasibility, friction cone, torque limits). The simulation results of the humanoid robot WALK-MAN demonstrate the feasibility of proposed control strategy with relatively high energy efficiency. A t ypical b utterfly sh ape of CoM trajectory was also observed in the frontal plane which is common in human walking.

show abstract

Planning COM trajectory with variable height and foot position with reactive stepping for humanoid robots

Cited by 12 publications

References 10 publications

A robust linear MPC approach to online generation of 3D biped walking motion

A robust linear MPC approach to online generation of 3D biped walking motion

Real-Time Variable Center of Mass Height Trajectory Planning for Humanoids Robots

Straight leg walking strategy for torque-controlled humanoid robots

Contact Info

Product

Resources

About