The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations.
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Wrench Analysis of Kinematically Redundant Planar CDPRs
A fully-constrained ๐โ๐ท๐๐น cable-driven parallel robot (CDPR) has wrench closure if there are ๐+1 cables exerting positive tensions spanning the wrench space. However, the quality of wrench closure is often dependent on the geometric configuration of the supporting in-parallel chains of the CDPR. The reconfigurability endowed by adding in-chain kinematic and/or actuation redundancy to a conventional cable robot could greatly improve quality of the workspace. However, the status of various joints (active, passive or locked) affect the complexity of the systematic formulation and ultimate wrench-based analysis. Past efforts have tended to equilibrate the forces in these systems in such a way as to avoid kinematic redundancies. To this end, we formulate the kinematics of the redundant reconfigurable CDPR using matrix Lie group formulation (to allow ease of formulation and subsequent generalizability). Reciprocity (and selective reciprocity) permits the development of wrench analyses including the partitioning of actuation vs structural equilibration components. The total wrench set is greatly expanded both by the addition of kinematic redundancy and selective actuation/locking of the joints. The approach adopted facilitates the holistic determination of the true wrench polytope which accounts for the wrench contributions from all actuation sources. All these aspects are examined with variants of a 4-PRPR planar cable driven parallel manipulator (with varied active/passive/locked joints).
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- NSF-PAR ID:
- 10280453
- Editor(s):
- Gouttefarde M.; Bruckmann T.; Pott A.
- Date Published:
- Journal Name:
- Cable-Driven Parallel Robots. CableCon 2021. Mechanisms and Machine Science
- Volume:
- 104
- Page Range / eLocation ID:
- 90-104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Background Previous research shows kinematic and kinetic coupling between the metatarsophalangeal (MTP) and midtarsal joints during gait. Studying the effects of MTP position as well as foot structure on this coupling may help determine to what extent foot coupling during dynamic and active movement is due to the windlass mechanism. This study's purpose was to investigate the kinematic and kinetic foot coupling during controlled passive, active, and dynamic movements.
Methods After arch height and flexibility were measured, participants performed four conditions: Seated Passive MTP Extension, Seated Active MTP Extension, Standing Passive MTP Extension, and Standing Active MTP Extension. Next, participants performed three heel raise conditions that manipulated the starting position of the MTP joint: Neutral, Toe Extension, and Toe Flexion. A multisegment foot model was created in Visual 3D and used to calculate ankle, midtarsal, and MTP joint kinematics and kinetics.
Results Kinematic coupling (ratio of midtarsal to MTP angular displacement) was approximately six times greater in Neutral heel raises compared to Seated Passive MTP Extension, suggesting that the windlass only plays a small kinematic role in dynamic tasks. As the starting position of the MTP joint became increasingly extended during heel raises, the amount of negative work at the MTP joint and positive work at the midtarsal joint increased proportionally, while distalโtoโhindfoot work remained unchanged. Correlations suggest that there is not a strong relationship between static arch height/flexibility and kinematic foot coupling.
Conclusions Our results show that there is kinematic and kinetic coupling within the distal foot, but this coupling is attributed only in small measure to the windlass mechanism. Additional sources of coupling include foot muscles and elastic energy storage and return within ligaments and tendons. Furthermore, our results suggest that the plantar aponeurosis does not function as a rigid cable but likely has extensibility that affects the effectiveness of the windlass mechanism. Arch structure did not affect foot coupling, suggesting that static arch height or arch flexibility alone may not be adequate predictors of dynamic foot function.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-75789-2_8
