An efficiently solvable quadratic program for stabilizing dynamic locomotion

Kuindersma, Scott; Permenter, Frank; Tedrake, Russell Louis

doi:10.1109/icra.2014.6907230

Cited by 179 publications

(139 citation statements)

References 20 publications

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“…Using these trajectories and a linear Time Variant LQR, the method solves for CoM dynamics over an arbitrary horizon and then CoM accelerations found are given to their low level active-set based QP solver to generate joint torques. The major difference of [11] with our method is the fact that we do not have any off-line optimization. Rather we optimize the next footstep positions on-line, considering the aforementioned constraints and a reference footstep pattern Fig.…”

Section: Introductionmentioning

confidence: 99%

“…Although the equality constraint of contact acceleration is considered in closed form solutions [19], one can not include inequality constraints like Center of Pressure (CoP), friction cones or joint torque limits easily. This motivates solving a quadratic constrained problem using fast QP solvers per time step where one can consider all constraints at the same time ( [6], [25], [24] and [11]). With such formulation of the joint controller, we can track desired trajectories at endeffectors with simple PD controllers while being compliant, maintaining balance and satisfying all constraints.…”

Section: Introductionmentioning

confidence: 99%

“…The novelty of this work is mainly in the third layer where we plan future footsteps in discrete space. In [11], first optimal trajectories are found off-line by inverse kinematics and a small QP for the configuration of the robot (based on [16]). Using these trajectories, the method proposed in [11] then finds optimal ZMP trajectories that satisfy robots frictional and torque limit constraints.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], first optimal trajectories are found off-line by inverse kinematics and a small QP for the configuration of the robot (based on [16]). Using these trajectories, the method proposed in [11] then finds optimal ZMP trajectories that satisfy robots frictional and torque limit constraints. Using these trajectories and a linear Time Variant LQR, the method solves for CoM dynamics over an arbitrary horizon and then CoM accelerations found are given to their low level active-set based QP solver to generate joint torques.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

Faraji

Pouya²,

Ijspeert³

2014

Robotics: Science and Systems X

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Abstract-In this paper, we formulate a novel hierarchical controller for walking of torque controlled humanoid robots. Our method uses an online whole body optimization approach which generates joint torques, given Cartesian accelerations of different points on the robot. Over such variable translation, we can plan our desired foot trajectories in Cartesian space between starting and ending positions of the foot on the ground. On top level, we use the simplified Linear Inverted Pendulum Model to predict the future motion of the robot. With LIPM, we derive a formulation where the whole system is described by the state of center of mass and footstep locations serve as discrete inputs to this linear system. We then use model predictive control to plan optimal future footsteps which resemble a reference plan, given desired sagittal and steering velocities determined by the high-end user. Using simulations on a child-size torque controlled humanoid robot, the method tolerates various disturbances such as external pushes, sensor noises, model errors and delayed communication in the control loop. It can perform robust walking over slopes and uneven terrains blindly and turn rapidly at the same time. Our generic dynamics model-based method does not depend on any off-line optimization, being suitable for typical torque controlled humanoid robots.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

Faraji

Pouya²,

Ijspeert³

2014

Robotics: Science and Systems X

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“…Drawing inspiration from other robotic fields (e.g., [13], [14]), in this paper we take advantage of a quadratic programming technique to solve several UAM tasks in real time, on board and subject to constraints. Specifically we use the online active set strategy ( [15], [16]) which analyses the constraints that are active at the current evaluation point, and gives us a subset of inequalities to watch while searching for the solution, which reduces the complexity of the search and thus the computation time.…”

mentioning

confidence: 99%

Trajectory Generation for Unmanned Aerial Manipulators Through Quadratic Programming

Rossi

Santamaria-Navarro

Andrade‐Cetto

et al. 2017

IEEE Robot. Autom. Lett.

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Abstract-In this paper a trajectory generation approach using quadratic programming is described for aerial manipulation, i.e. for the control of an aerial vehicle equipped with a robot arm. The proposed approach applies the online active set strategy to generate a feasible trajectory of the joints, in order to accomplish a set of tasks with defined bounds and constraint inequalities. The definition of the problem in the acceleration domain allows to integrate and perform a large set of tasks and, as a result, to obtain smooth motion of the joints. A weighting strategy, associated with a normalization procedure, allows to easily define the relative importance of the tasks. This approach is useful to accomplish different phases of a mission with different redundancy resolution strategies. The performance of the proposed technique is demonstrated through real experiments with all the algorithms running onboard in real time. In particular, the aerial manipulator can successfully perform navigation and interaction phases, while keeping motion within prescribed bounds and avoiding collisions with external obstacles.

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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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An efficiently solvable quadratic program for stabilizing dynamic locomotion

Cited by 179 publications

References 20 publications

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

Robust and Agile 3D Biped Walking With Steering Capability Using a Footstep Predictive Approach

Trajectory Generation for Unmanned Aerial Manipulators Through Quadratic Programming

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

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