Planning robust walking motion on uneven terrain via convex optimization

Abstract-Traditional motion planning approaches for multilegged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion robustness while keeping a low computation time.

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“…We describe the evolution of the system using a centroidal dynamics model [15], [16], as depicted in Fig. 3.…”

Section: B Centroidal Dynamicsmentioning

confidence: 99%

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

Aceituno-Cabezas

Mastalli

Dai

et al. 2017

IEEE Robot. Autom. Lett.

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106

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“…the proxy can be written as the constraint to have the state variables in the range space of γ. Set-membership proxies are used for instance in [11,7] to encode maximal step size in biped walking, or in [5] to bound the CoM position by simple geometric shape. In all these cases, the set boundaries are represented by very simple mathematical structures (typically linear inequalities) in order not to burden the OCP solver.…”

Section: A Mathematical Representation Of Feasibility Constraintsmentioning

confidence: 99%

“…b) Centroidal resolution: From the contact sequence and the learned CoM feasibility constraints, we solve the optimal control formulation (3) with the tailored cost function (5). For all the experiments and robots, we use the same weighting in the cost function: w x = 10.…”

Section: B Complete Pipelinementioning

confidence: 99%

“…Direct resolution of the underlying optimal control problem based on multiple-shooting approach has been recently proposed [4], leading to real-time performances. Other contributions have also been suggested that exhibit approximate dynamics (with possibly bounded approximations) leading to convex optimization problems, thus ensuring global optimality [13,5,2]. In most cases, the footstep sequence is assumed given, although some solvers are also able to discover it while optimizing the centroidal dynamics [19,7], to the price of heavier computational costs.…”

Section: Introductionmentioning

confidence: 99%

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Learning Feasibility Constraints for Multicontact Locomotion of Legged Robots

Carpentier¹,

Budhiraja²,

Mansard³

2017

Robotics: Science and Systems XIII

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Abstract-Relying on reduced models is nowadays a standard cunning to tackle the computational complexity of multi-contact locomotion. To be really effective, reduced models must respect some feasibility constraints in regards to the full model. However, such kind of constraints are either partially considered or just neglected inside the existing reduced problem formulation. This work presents a systematic approach to incorporate feasibility constraints inside trajectory optimization problems. In particular, we show how to learn the kinematic feasibility of the centre of mass to be achievable by the whole-body model. We validate the proposed method in the context of multi-contact locomotion: we perform two stairs climbing experiments on two humanoid robots, namely the HRP-2 robot and the new TALOS platform.

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“…One possible aim is to reduce the probability of failure [1], [6], [7]. But here, we aim at ensuring the correct operation of the system for any uncertainty between certain bounds.…”

Section: Introductionmentioning

confidence: 99%

Model predictive control of biped walking with bounded uncertainties

Villa

Wieber

2017

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

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Abstract-A biped walking controller for humanoid robots has to handle together hard constraints, dynamic environments, and uncertainties. Model Predictive Control (MPC) is a suitable and widely used control method to handle the first two issues. Uncertainties on the robot imply a non-zero tracking error when trying to follow a reference motion. A standard solution for this issue is to use tighter constraints by introducing some hand tuned safety margins, for the reference motion generation to ensure that the actual robot motion will satisfy all constraints even in presence of the tracking error. In this article, we find bounds for the tracking error and we show how such safety margins can be precisely computed from the tracking error bounds. Also, a tracking control gain is proposed to reduce the restrictiveness introduced with the safety margins. MPC with these considerations ensure the correct operation of the biped robot under a given degree of uncertainties when it is implemented in open-loop. Nevertheless, the straightforward way to implement an MPC closed-loop scheme fails. We discuss the reasons for this failure and propose a robust closed-loop MPC scheme.

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Planning robust walking motion on uneven terrain via convex optimization

Cited by 114 publications

References 25 publications

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

Learning Feasibility Constraints for Multicontact Locomotion of Legged Robots

Model predictive control of biped walking with bounded uncertainties

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