Model predictive control for dynamic footstep adjustment using the divergent component of motion

Griffin, Robert J.; Leonessa, Alexander

doi:10.1109/icra.2016.7487320

Cited by 31 publications

(40 citation statements)

References 22 publications

(53 reference statements)

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“…Eqs. (2) and (3) show how the CoM state evolves after time t, from the initial state x(0) x(0) T to the final state x(t) x(t) T ; we use vector x to denote the CoM state x x T .…”

Section: Preliminariesmentioning

confidence: 99%

Comparison Study of Nonlinear Optimization of Step Durations and Foot Placement for Dynamic Walking

Chatzinikolaidis

Yuan

et al. 2018

2018 IEEE International Conference on Robotics and Automation (ICRA)

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This paper studies bipedal locomotion as a nonlinear optimization problem based on continuous and discrete dynamics, by simultaneously optimizing the remaining step duration, the next step duration and the foot location to achieve robustness. The linear inverted pendulum as the motion model captures the center of mass dynamics and its lowdimensionality makes the problem more tractable. We first formulate a holistic approach to search for optimality in the three-dimensional parametric space and use these results as baseline. To further improve computational efficiency, our study investigates a sequential approach with two stages of customized optimization that first optimizes the current step duration, and subsequently the duration and location of the next step. The effectiveness of both approaches is successfully demonstrated in simulation by applying different perturbations. The comparison study shows that these two approaches find mostly the same optimal solutions, but the latter requires considerably less computational time, which suggests that the proposed sequential approach is well suited for real-time implementation with a minor trade-off in optimality.

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“…Eqs. (2) and (3) show how the CoM state evolves after time t, from the initial state x(0) x(0) T to the final state x(t) x(t) T ; we use vector x to denote the CoM state x x T .…”

Section: Preliminariesmentioning

confidence: 99%

Comparison Study of Nonlinear Optimization of Step Durations and Foot Placement for Dynamic Walking

Chatzinikolaidis

Yuan

et al. 2018

2018 IEEE International Conference on Robotics and Automation (ICRA)

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“…To address the above problem, Krausse et al, [14] suggested a formulation of the CP controller within MPC framework. Using MPC, the 3D extension of the CP called divergence component of motion (DCM) is controlled in [15] for the ajustment of footstep positions and orientations in the presence of disturbance. In [16], a CP based MPC is used for push recovery.…”

Section: A Related Workmentioning

confidence: 99%

“…Unlike in [23], [14], [15], [17] where the reference footsteps were predetermined, in this work, they are formulated as variables such that they can be generated automatically on-line. To that end, let us consider that there are only four (m = 4) footsteps (f 1 , f 2 , f 3 , f 4 ) falling within the receding horizon N (it only eases the computation of the CoM's average velocity in the rest of these developments).…”

Section: Self-generated Capture-point Reference Trajectoriesmentioning

confidence: 99%

Capture-point based balance and reactive omnidirectional walking controller

Bombile

Billard

2017

2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids)

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Abstract-This paper proposes a capture-point based reactive omnidirectional controller for bipedal locomotion. The proposed scheme, formulated within Model Predictive Control (MPC) framework, exploits concurrently the Center of Mass (CoM) and Capture Point (CP) dynamics. It allows the on-line generation of the CoM reference trajectory and the automatic generation of footstep positions and orientations in response to a given velocity to be tracked, or a disturbance to be rejected by the robot while accounting explicitly for different walking constraints. For instance, in order to cope with disturbance such as a push, the proposed controller not only adjusts the position of the Center of Pressure (CoP) within the support foot, but can also induce at least one step with appropriate length allowing thus to maintain the stability of the robot. Finally, the proposed algorithm is validated through simulations and actual experiments on the humanoid robot iCub.

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“…Moreover, the MPC approach guarantees a certain robustness against perturbations. It is therefore not surprising that it has been adopted in many methods for gait generation; e.g., see [8], [9], [10], [11] for linear MPC and [12], [13] for nonlinear MPC.…”

Section: Introductionmentioning

confidence: 99%

MPC for Humanoid Gait Generation: Stability and Feasibility

et al. 2020

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We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation. The proposed method uses as prediction model a dynamically extended LIP where ZMP velocities are the control inputs, producing in real time a gait (including footsteps with the associated timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links the future ZMP velocities to the current system state so as to guarantee the essential requirement that the generated CoM trajectory is bounded with respect to the ZMP trajectory. Since the control horizon of the MPC algorithm is finite, only part of the future ZMP velocities are decision variables of the QP problem; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint. A theoretical analysis of the feasibility of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, it is proved that IS-MPC guarantees stability of the CoM/ZMP dynamics if it is recursively feasible. Simulation and experimental results on the NAO and the HRP-4 humanoids are presented to illustrate the performance of the proposed method.

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Model predictive control for dynamic footstep adjustment using the divergent component of motion

Cited by 31 publications

References 22 publications

Comparison Study of Nonlinear Optimization of Step Durations and Foot Placement for Dynamic Walking

Comparison Study of Nonlinear Optimization of Step Durations and Foot Placement for Dynamic Walking

Capture-point based balance and reactive omnidirectional walking controller

MPC for Humanoid Gait Generation: Stability and Feasibility

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