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Direct Collocation Methods for Trajectory Optimization in Constrained Robotic Systems
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DOI：10.1109/TRO.2022.3193776.png)
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Abstract
En 中文
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained mechanical systems, i.e., those whose state coordinates are subject to holonomic or nonholonomic constraints, such as loop-closure or rolling-contact constraints. These constraints confine the robot trajectories to an implicitly-defined manifold, which complicates the computation of accurate solutions. Discretization errors inherent to the transcription of the problem easily make the trajectories drift away from this manifold, which results in physically inconsistent motions that are difficult to track with a controller. This article reviews existing methods to deal with this problem and proposes new ones to overcome their limitations. Current approaches either disregard the kinematic constraints (which leads to drift accumulation) or modify the system dynamics to keep the trajectory close to the manifold (which adds artificial forces or energy dissipation to the system). The methods we propose, in contrast, achieve full drift elimination on the discrete trajectory, or even along the continuous one, without artificial modifications of the system dynamics. We illustrate and compare the methods using various examples of different complexity.
Keywords:
Trajectory
Manifolds
Robot kinematics
Kinematics
System dynamics
Mathematical models
Collision avoidance
Constrained system
direct collocation
holonomic constraints
local coordintes
motion planning
nonholonomic constraints
trajectory optimization
Journal
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