Adaptive step duration in biped walking: A robust approach to nonlinear constraints

Bohorquez, Nestor; Wieber, Pierre-Brice

doi:10.1109/humanoids.2017.8246952

Cited by 7 publications

(10 citation statements)

References 13 publications

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“…First, we consider that the robot can directly control the jerk (i.e., the derivative of acceleration)

\overset{⃛}{x}

of its CoM, a standard assumption within the humanoid robot walking literature, 27-29 thus the CoM evolution is dictated by:

\frac{d}{d t} [\begin{matrix} x \\ \overset{x}{true} \\ \overset{x}{true} \end{matrix}] = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}] [\begin{matrix} x \\ \overset{x}{true} \\ \overset{x}{true} \end{matrix}] + [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \overset{⃛}{x} .

…”

Section: Optimal Control Formulationmentioning

confidence: 99%

“…The ZMP position is constrained to lie within the support polygon by using the support foot position. We consider that the double support phase lasts exactly one time step, which refrains us from explicitly modeling double support, an assumption that is wide‐spread within the humanoid walking literature 16,27-29 . Therefore, the ZMP constraints employ the support foot center at each time step i together with the respective chosen foot rotation:

{(θ_{f}^{a u x} [k])}_{i, m} \Rightarrow d_{s} (θ_{f, m}^{p} [k]) [\begin{matrix} {boldr}_{Z M P, x} false[k + i false| k false] prefix- x_{f, i}^{a u x} false[k false] \\ {boldr}_{Z M P, y} false[k + i false| k false] prefix- y_{f, i}^{a u x} false[k false] \end{matrix}] \leq s, 1 \leq i \leq N, 1 \leq m \leq N_{r},

where

d_{s} (θ_{f, m}^{p} [k])

projects the ZMP error on the directions of the vectors normal to the sides of the support polygon when the foot is oriented with the m th rotation in

Θ_{f}^{p}

and s contains the maximum ZMP error allowed by the support polygon in each direction.…”

Section: Optimal Control Formulationmentioning

confidence: 99%

“…For a more detailed discussion, please refer to Appendix F. In our particular implementation, we consider the foot to be a rectangle with length l and width w , which is both a good approximation for most humanoid robots and a common modeling approach within the literature, 27-29 thus:

d_{s} (θ) = [\begin{matrix} normalcos false(θ false) & normalsin false(θ false) \\ prefix- normalcos false(θ false) & prefix- normalsin false(θ false) \\ prefix- normalsin false(θ false) & normalcos false(θ false) \\ normalsin false(θ false) & normalcos false(θ false) \end{matrix}], s = [\begin{matrix} l false/ 2 \\ l false/ 2 \\ w false/ 2 \\ w false/ 2 \end{matrix}] .

…”

Section: Optimal Control Formulationmentioning

confidence: 99%

“…Bohórquez and Wieber 27 proposed a controller with step duration decision using concepts from robust control to guarantee constraint satisfaction using more conservative linear constraints instead of nonlinear ones. Nonetheless, their method adapts the sample time, making all steps within the prediction horizon be shortened or enlarged simultaneously.…”

Section: Introductionmentioning

confidence: 99%

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Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Máximo

Afonso

2020

Optim Control Appl Methods

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Summary This paper presents a mixed‐integer model predictive controller for walking. In the proposed scheme, mixed‐integer quadratic programs (MIQP) are solved online to simultaneously decide center of mass jerks, footsteps positions, durations, and rotations while respecting actuation, geometry, and contact constraints. Most walking controllers require preplanned footstep rotations to avoid dealing with the nonlinearity introduced by foot rotation decision. The main contribution of this work is an optimization formulation where feet rotations are automatically planned to attain a reference speed rotation. Finally, simulation results are shown to present and discuss the capabilities of the proposed formulation.

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“…First, we consider that the robot can directly control the jerk (i.e., the derivative of acceleration)

\overset{⃛}{x}

of its CoM, a standard assumption within the humanoid robot walking literature, 27-29 thus the CoM evolution is dictated by:

\frac{d}{d t} [\begin{matrix} x \\ \overset{x}{true} \\ \overset{x}{true} \end{matrix}] = [\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}] [\begin{matrix} x \\ \overset{x}{true} \\ \overset{x}{true} \end{matrix}] + [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}] \overset{⃛}{x} .

…”

Section: Optimal Control Formulationmentioning

confidence: 99%

{(θ_{f}^{a u x} [k])}_{i, m} \Rightarrow d_{s} (θ_{f, m}^{p} [k]) [\begin{matrix} {boldr}_{Z M P, x} false[k + i false| k false] prefix- x_{f, i}^{a u x} false[k false] \\ {boldr}_{Z M P, y} false[k + i false| k false] prefix- y_{f, i}^{a u x} false[k false] \end{matrix}] \leq s, 1 \leq i \leq N, 1 \leq m \leq N_{r},

where

d_{s} (θ_{f, m}^{p} [k])

projects the ZMP error on the directions of the vectors normal to the sides of the support polygon when the foot is oriented with the m th rotation in

Θ_{f}^{p}

and s contains the maximum ZMP error allowed by the support polygon in each direction.…”

Section: Optimal Control Formulationmentioning

confidence: 99%

d_{s} (θ) = [\begin{matrix} normalcos false(θ false) & normalsin false(θ false) \\ prefix- normalcos false(θ false) & prefix- normalsin false(θ false) \\ prefix- normalsin false(θ false) & normalcos false(θ false) \\ normalsin false(θ false) & normalcos false(θ false) \end{matrix}], s = [\begin{matrix} l false/ 2 \\ l false/ 2 \\ w false/ 2 \\ w false/ 2 \end{matrix}] .

…”

Section: Optimal Control Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Máximo

Afonso

2020

Optim Control Appl Methods

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show abstract

“…adapting the duration of steps [18] and the vertical motion of the CoM [19] [20]. It has also been used for the adaptation of the rotation of the steps [21] but, in comparison, we propose constraints that generate less restrictive motions.…”

Section: Introductionmentioning

confidence: 99%

Adaptive step rotation in biped walking

Bohorquez

Wieber

2018

2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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We want to enable the robot to reorient its feet in order to face its direction of motion. Model Predictive Control schemes for biped walking usually assume fixed feet rotation since adapting them online leads to a nonlinear problem. Nonlinear solvers do not guarantee the satisfaction of nonlinear constraints at every iterate and this can be problematic for the real-time operation of robots. We propose to define safe linear constraints that are always inside the intersection of the nonlinear constraints. We make simulations of the robot walking on a crowd and compare the performance of the proposed method with respect to the original nonlinear problem solved as a Sequential Quadratic Program.

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Online Robust Gait Generator of Biped Robots Inspired by Human Anti-disturbance Strategies

Yuan

Dong

et al. 2022

J Intell Robot Syst

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Adaptive step duration in biped walking: A robust approach to nonlinear constraints

Cited by 7 publications

References 13 publications

Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Adaptive step rotation in biped walking

Online Robust Gait Generator of Biped Robots Inspired by Human Anti-disturbance Strategies

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