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This paper reports a novel result: with proper robot models based on geometric mechanics, one can formulate the kinodynamic motion planning problems for rigid body systems as exact polynomial optimization problems. Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not parameterize 3D rigid body motion efficiently; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space and apply the variational integrator to formulate the forced rigid body dynamics as quadratic polynomials. Then, we leverage Lasserre’s hierarchy of moment relaxation to obtain the globally optimal solution via semidefinite programming. By leveraging the sparsity of the motion planning problem, the proposed algorithm has linear complexity with respect to the planning horizon. This paper demonstrates that the proposed method can provide globally optimal solutions or certificates of infeasibility at the second-order relaxation for 3D drone landing using full dynamics and inverse kinematics for serial manipulators. Moreover, we extend the algorithms to multi-body systems via the constrained variational integrators. The testing cases on cart-pole and drone with cable-suspended load suggest that the proposed algorithms can provide rank-one optimal solutions or nontrivial initial guesses. Finally, we propose strategies to speed up the computation, including an alternative formulation using quaternion, which provides empirically tight relaxations for the drone landing problem at the first-order relaxation.
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Development and Optimization of a Noncircular Pulley for Motion Decoupling in Cable-Driven Serial Robots
Abstract Cable-driven serial robots have emerged with high potential for wide applications due to their compact size and low inertia properties. However, developing this type of robot encounters a motion coupling issue that the movement of one joint leads to the motion of other joints, resulting in complex control. In this paper, we proposed a novel approach for motion decoupling based on a noncircular pulley. The length change of the driving cable caused by the motion coupling problem is resolved by using the noncircular pulley. The calculation process of the profile for the noncircular pulley is illustrated in detail. An optimization process based on the brute force method is presented to identify the optimal parameters to minimize the compensation error. A cable-driven serial robot based on the decoupling method is prototyped for assessments. Experiments are conducted to evaluate the performance of the proposed motion decoupling method. The results reveal that the proposed method can effectively resolve the motion coupling issue by maintaining almost constant cable length with a maximum accumulative error only as 0.086 mm, demonstrating the effectiveness of the method.
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- Award ID(s):
- 2138903
- PAR ID:
- 10573379
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- Journal of Mechanical Design
- Volume:
- 146
- Issue:
- 11
- ISSN:
- 1050-0472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4065278
