An enhanced inverse dynamics approach is here presented for feedforward control of underactuated multibody systems, such as mechanisms or robots where the number of independent actuators is smaller than the number of degrees of freedom. The method exploits the concept of partitioning the independent coordinates into actuated and unactuated ones (through a QR-decomposition) and of linearly combined output, to obtain the internal dynamics of the nonminimum-phase system and then to stabilize it through proper output redefinition. Then, the exact algebraic model of the actuated sub-system is inverted, by leading to the desired control forces with just minor approximations and no need of pre-actuation. The effectiveness of the proposed approach is assessed by three numerical test cases, by comparing it with some meaningful benchmarks taken from the literature. Finally, experimental verification through an underactuated robotic arm with two degrees of freedom is performed.
Purpose
This paper proposes a motion planning technique for precise path and trajectory tracking in an underactuated, non-minimum phase, spatial overhead crane. Besides having a number of independent actuators that is smaller than the number of degrees of freedom, tip control on this system presents unstable internal dynamics that leads to divergent solution of the inverse dynamic problem.
Method
The paper exploits the representation of the controlled output as a separable function of the actuated (i.e., the platform translations) and unactuated (i.e., the swing angles) coordinates to easily formulate the internal dynamics, without any approximation, and to study its stability. Then, output redefinition is adopted within the internal dynamics to stabilize it, leading to stable and causal reference commands for the platform translations.
Results
Besides proposing the theoretical formulation of this novel method, the paper includes the numerical validation and the experimental application on a laboratory setup. Comparison with the state-of-the-art input shaping is also proposed.
Conclusion
The results, obtained through different reference trajectories, clearly show that almost exact tracking is obtained also in the experiments, by outperforming the benchmarks.
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