Motion planning with sequential convex optimization and convex collision checking

Schulman, John; Duan, Yan; Ho, Jonathan; Lee, Alex; Awwal, Ibrahim; Bradlow, Henry; Pan, Jia; Patil, Sachin; Goldberg, Ken; Abbeel, Pieter

doi:10.1177/0278364914528132

Cited by 684 publications

(509 citation statements)

References 72 publications

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“…For the cases of no intersection points with the ith obstacle in g 1 (c The above framework works well in analytically solving the constrained optimization problem in (44). However, as a trade-off, such a method is based on a set of finite lines that impose an additional constraint as (45) to the suboptimal solutions, which may ignore solutions that actually exist while not satisfying the additional constraint. Here we introduce an alternative technique to numerically solve the problem (44), which maybe less efficient while could potentially find more feasible solutions.…”

Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

“…Such an algorithm is one of the most effective methods for nonlinearly constrained optimization problems. The idea is that at each iteration, a locally quadratic approximation of the objective is made using a quasi-Newton updating method and a quadratic programming(QP) subproblem is generated with locally linearized constraints whose solution is then used for a line search procedure [44] [45]. Since SQP can deal with infeasible initializations, we can directly set up the initial searching point by the optimal solution O k * (c k *…”

Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

“…It is worth noting that besides the complexity of the inequality constraints due to (41), the computational complexity and the quality of solutions also largely depends on the pre-defined stepsize and tolerance for searching, which maybe hard to properly determine given the complicated obstacle information and different task settings. Given the good analytical property of the results in (49), the method of SQP could be considered as a complementary technique in the extreme situation that all the feasible solutions to (44) are only located in the positions that do not satisfy the additional constraint (45). ♢…”

Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

See 2 more Smart Citations

A suboptimal and analytical solution to mobile robot trajectory generation amidst moving obstacles

et al. 2015

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Abstract-In this paper, we present a suboptimal and analytical solution to the trajectory generation of mobile robots operating in a dynamic environment with moving obstacles. The proposed solution explicitly addresses both the robot kinodynamic constraints and the geometric constraints due to obstacles while ensuring the suboptimal performance to a combined performance metric. In particular, the proposed design is based on a family of parameterized trajectories, which provides a unified way to embed the kinodynamic constraints, geometric constraints, and performance index into a set of parameterized constraint equations. To that end, the suboptimal solution to the constrained optimization problem can be analytically obtained. The solvability conditions to the constraint equations are explicitly established, and the proposed solution enhances the methodologies of real-time path planning for mobile robots with kinodynamic constraints. Both the simulation and experiment results verify the effectiveness of the proposed method.

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Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

Section: Suboptimal Solution To the Constrained Optimization Problmentioning

confidence: 99%

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A suboptimal and analytical solution to mobile robot trajectory generation amidst moving obstacles

et al. 2015

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“…Kanehiro et. al [11,12] show the use of QPs to incorporate fast collision avoidance calculations as part of humanoid whole body motion planning. Our method incorporates many additional constraints and optimality criteria, and our explicit formulation of several key kinematic equations [13] gives us significant advantanges in terms of reported computation time (even adjusting for Moore's law).…”

Section: Introductionmentioning

confidence: 99%

A Quadratic Programming Approach to Quasi-Static Whole-Body Manipulation

Shankar

Burdick

Hudson

2015

Springer Tracts in Advanced Robotics

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Abstract. This paper introduces a local motion planning method for robotic systems with manipulating limbs, moving bases (legged or wheeled), and stance stability constraints arising from the presence of gravity. We formulate the problem of selecting local motions as a linearly constrained quadratic program (QP), that can be solved efficiently. The solution to this QP is a tuple of locally optimal joint velocities. By using these velocities to step towards a goal, both a path and an inverse-kinematic solution to the goal are obtained. This formulation can be used directly for real-time control, or as a local motion planner to connect waypoints. This method is particularly useful for high-degree-of-freedom mobile robotic systems, as the QP solution scales well with the number of joints. We also show how a number of practically important geometric constraints (collision avoidance, mechanism self-collision avoidance, gaze direction, etc) can be readily incorporated into either the constraint or objective parts of the formulation. Additionally, motion of the base, a particular joint, or a particular link can be encouraged/discouraged as desired. We summarize the important kinematic variables of the formulation, including the stance Jacobian, the reach Jacobian, and a center of mass Jacobian. The method is easily extended to provide sparse solutions, where the fewest number of joints are moved, by iteration using Tibshirani's method to accommodate an l1 regularizer. The approach is validated and demonstrated on SURROGATE, a mobile robot with a TALON base, a 7 DOF serial-revolute torso, and two 7 DOF modular arms developed at JPL/Caltech.

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“…Several related methods [17,18,19,30] extend Hierarchical Task Networks (HTN) [26] with geometric primitives, using shared literals to control backtracking between the task and motion layer. [72] interfaces off-the-shelf task planners with an optimization-based motion planner [70] using a heuristic to remove potentially-interfering objects. [57] formulates the motion side of TMP as a constraint satisfaction problem over a discretized, preprocessed subset of the configuration space.…”

Section: Task and Motion Planningmentioning

confidence: 99%

Incremental Task and Motion Planning: A Constraint-Based Approach

Dantam¹,

Kingston²,

Chaudhuri³

et al.

Robotics: Science and Systems XII

149

115

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Abstract-We present a new algorithm for task and motion planning (TMP) and discuss the requirements and abstractions necessary to obtain robust solutions for TMP in general. Our Iteratively Deepened Task and Motion Planning (IDTMP) method is probabilistically-complete and offers improved performance and generality compared to a similar, state-of-theart, probabilistically-complete planner. The key idea of IDTMP is to leverage incremental constraint solving to efficiently add and remove constraints on motion feasibility at the task level. We validate IDTMP on a physical manipulator and evaluate scalability on scenarios with many objects and long plans, showing order-of-magnitude gains compared to the benchmark planner and a four-times self-comparison speedup from our extensions. Finally, in addition to describing a new method for TMP and its implementation on a physical robot, we also put forward requirements and abstractions for the development of similar planners in the future.

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Motion planning with sequential convex optimization and convex collision checking

Abstract: Abstract

Cited by 684 publications

References 72 publications

A suboptimal and analytical solution to mobile robot trajectory generation amidst moving obstacles

A suboptimal and analytical solution to mobile robot trajectory generation amidst moving obstacles

A Quadratic Programming Approach to Quasi-Static Whole-Body Manipulation

Incremental Task and Motion Planning: A Constraint-Based Approach

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