On time optimal path control of manipulators with bounded joint velocities and torques

Žlajpah, Leon

doi:10.1109/robot.1996.506928

Cited by 64 publications

(63 citation statements)

References 9 publications

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“…Using acceleration instead of torque limits results in a simpler problem and a simpler derivation of the following equations than in [5]. Unlike [5] and like [9], we are also considering velocity limits on the joints. Because the solution is constrained to follow a given path exactly, the problem can be reduced to one dimension: choosing the velocityṡ = ds dt for every position s along the path.…”

Section: Path Preprocessingmentioning

confidence: 99%

“…We now describe how numerical inaccuracies can make the algorithm described in section Section VI fail and the measures we have taken to avoid that. None of the previous papers on this approach [5][6][7][8][9] have dealt with numerical issues.…”

Section: B Caused By Velocity Constraintsmentioning

confidence: 99%

“…The inaccurate trajectory, however, because of the larger step size, misses the bend shortly before the limit curve and hits the limit curve. According to the algorithm described in Section VI and the algorithms described in previous work [5,6,8,9] we would have to stop the forward integration, search for the next switching point along the limit curve and integrate backward from there until we hit the forward trajectory. However, when integrating backwardṡ from the next switching point we might hit the limit curve instead of the forward trajectory.…”

Section: A Integrationmentioning

confidence: 99%

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Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

Kunz¹,

Stilman²

2012

Robotics: Science and Systems VIII

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Abstract-This paper presents a novel method to generate the time-optimal trajectory that exactly follows a given differentiable joint-space path within given bounds on joint accelerations and velocities. We also present a path preprocessing method to make nondifferentiable paths differentiable by adding circular blends. We introduce improvements to existing work that make the algorithm more robust in the presence of numerical inaccuracies. Furthermore we validate our methods on hundreds of randomly generated test cases on simulated and real 7-DOF robot arms. Finally, we provide open source software that implements our algorithms.

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Section: Path Preprocessingmentioning

confidence: 99%

Section: B Caused By Velocity Constraintsmentioning

confidence: 99%

Section: A Integrationmentioning

confidence: 99%

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Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

Kunz¹,

Stilman²

2012

Robotics: Science and Systems VIII

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“…We can observe that it is very close to the analytical solution found in section III. The very small difference between these two solutions can be identified to be solely due to the discretization process (16)- (18). For the same reason, the approximate computation in (25) of the constraint (24) appears to slightly underestimate the limiting temperature constraint in this specific case, allowing a faster solution here than the truly optimal solution described in section III, with only 1.35s of cycle time rather than 1.38s in section III.…”

Section: A Numerical Resultsmentioning

confidence: 92%

“…The gradients can be calculated numerically with finite differences methods, but that severely impedes the convergence of the SQP. Symbolic or automatic differentiation methods [17] can be used also, but in our problem the geometric path is fixed and the dynamics (14) can be formulated very simply as [4] [3] [18]:…”

Section: B Optimization Algorithmmentioning

confidence: 99%

Optimal Trajectory Generation for Manipulator Robots under Thermal Constraints

Guilbert

Wieber

Joly

2006

2006 IEEE/RSJ International Conference on Intelligent Robots and Systems

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We propose here to deal with the optimization of velocity profiles of manipulator robots with a minimum time criterion subject to thermal constraints. This paper deals with the real impact of thermal limitations on optimal velocity profiles and the methods to calculate the corresponding optimal trajectories. We first calculate analytically the optimal solution in a simple case in order to verify the validity of the numerical algorithm and also to present a general methodology to calculate optimal trajectories in robotics using results from the theory of calculus of variations and not from the theory of optimal control. We derive then a numerical algorithm based on the discretization of the time law through an interpolation with non uniform cubic splines. This algorithm shows robust and efficient convergence properties and the trajectories thus generated were executed successfully on a Stäubli Rx90.

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A General Algorithm for Time-Optimal Trajectory Generation Subject to Minimum and Maximum Constraints

Butler

Moll

Kavraki

2020

Springer Proceedings in Advanced Robotics

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This paper presents a new algorithm which generates time-optimal trajectories given a path as input. The algorithm improves on previous approaches by generically handling a broader class of constraints on the dynamics. It eliminates the need for heuristics to select trajectory segments that are part of the optimal trajectory through an exhaustive, but efficient search. We also present an algorithm for computing all achievable velocities at the end of a path given an initial range of velocities. This algorithm effectively computes bundles of feasible trajectories for a given path and is a first step toward a new generation of more efficient kinodynamic motion planning algorithms. We present results for both algorithms using a simulated WAM arm with a Barrett hand subject to dynamics constraints on joint torque, joint velocity, momentum, and end effector velocity. The new algorithms are compared with a state-of-the-art alternative approach.

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On time optimal path control of manipulators with bounded joint velocities and torques

Cited by 64 publications

References 9 publications

Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

Optimal Trajectory Generation for Manipulator Robots under Thermal Constraints

A General Algorithm for Time-Optimal Trajectory Generation Subject to Minimum and Maximum Constraints

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