Quadratic programming for inverse kinematics control of a hexapod robot with inequality constraints

Kinematically redundant manipulators are advantageous for their increased dexterity and ability to fulfill some secondary requirements along with their primary task to follow the prescribed trajectory. The redundancy results in a non-trivial inverse kinematics problem (IK). Standard methods of redundancy resolution are based on the pseudoinverse of the Jacobian matrix of the manipulator. The excessive degrees of freedom are utilized to perform secondary tasks that are projected onto the null space of the Jacobian matrix. However, the joint constraints satisfaction cannot be easily ensured in this way-even though methods that account for the joint position limits are known, the constraints for joint velocities and especially accelerations are not straightforward to include. In this paper, a novel redundancy resolution method based on a less common quadratic programming (QP) approach is described. The proposed velocity-level IK method allows fulfilment of the joint constraints at the position, velocity, and acceleration levels. In the derived formulas, accelerations instead of the usual velocities are used-the discretized joint state equations allow the use of joint accelerations as decision variables in the QP problem. The developed algorithm is investigated in a series of numerical tests in which the kinematics of the KUKA LWR4+ redundant 7-DOF manipulator is exploited. The newly elaborated QP-based IK method is firstly compared with the classic pseudoinverse-based approach and then tested for its ability to keep the joint accelerations within the prescribed bounds. The prospects of the proposed approach are discussed in the concluding section.

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“…The QP formulation of IK problem is not limited to manipulators. It can also be used in mobile robots such as humanoids [42] or hexapods [43].…”

Section: Quadratic Programming Formulation Of the Inverse Kinematicsmentioning

confidence: 99%

A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

Woliński

Wojtyra

2022

IEEE Access

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“…(27) and Eq. (23) together constitute a QP problem, which can be solved by the method of interior point or active set [25].…”

Section: Conversion Of Probabilistic Constraints Based On Multiplementioning

confidence: 99%

An Output Probabilistic Constrained Optimal Control Algorithm Based on Multivariable MAC and its Application in Looper Control System

2019

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Most actual industrial processes are multivariable and constrained complex systems. The state and output of the system also have uncertainty due to the existence of random disturbances. The output of the system is easier to be measured than the state and can more intuitively reflect the running state of the system. Considering the limitations of industrial equipment and the benefits of production, it is generally allowed to have a small portion of the output that can exceed the constraints. As a result, the outputs can be represented as corresponding single probabilistic constraints. In this paper, therefore, an output probabilistic constrained optimal control algorithm based on multivariable model algorithm control (MMAC) is proposed. First, the feedback correction link of the MMAC algorithm is improved, and the predicted outputs are corrected by taking the weighted average of the errors. Then, assuming that the disturbances obey Gaussian distribution, the output probabilistic constraints are transformed into deterministic ones. Next, the optimal control problem is solved as a quadratic programming (QP) problem after combining them with the performance index function of the MMAC. Finally, the proposed algorithm is applied to the looper control system in hot strip rolling process and compared with the single MMAC algorithm to verify its effectiveness. INDEX TERMS Uncertainty, MMAC, output probabilistic constraints, feedback correction, looper control system.

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“…The contact points change over time depending on the maneuver being performed and, therefore, cannot be prespecified [14]. Considering the whole-body in the operational space of tasks, the transition from one posture to another is an activity sensitive to the accumulation of uncertainties in actuation [15]. A complex set of sensors and multiple layers of software cause noise and latencies in the transfer of information [16].…”

Section: Introductionmentioning

confidence: 99%

Flexibility in Hexapod Robots: Exploring Mobility of the Body

Bachega,

Neves,

Campo

et al. 2023

IEEE Access

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Introducing Myrmex, a hexapod robot designed for autonomous locomotion on unstructured terrains. It was developed a whole-body kinematics model that enables both open-chain and closed-chain control of the robot. This model enhances the flexibility and mobility of the robot. At the moment, Myrmex relies solely on proprioception (encoders and IMU) for adapting its body posture. Despite these sensory limitations, we have successfully applied the model in static and dynamic situations. Static experiments have showcased increased flexibility, allowing the robot to access previously challenging locations. In dynamic scenarios, the hexapod has demonstrated its capability to traverse irregular terrains, effectively exploiting its body mobility. Myrmex adeptly adjusts its posture according to the terrain topology, maintaining the center of gravity projection along the body's centerline (i.e., same as it in the level walk), thus preserving stability margins during gait. The robot was able to correct its posture on terrain with gradients in any direction relative to the body structure, with only 3 DoF per leg. Importantly, our experiments have underscored the robot's ability to maintain its posture even in the face of unexpected disturbances in its legs, emphasizing the robustness and reliability of the model.

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Quadratic programming for inverse kinematics control of a hexapod robot with inequality constraints

Cited by 12 publications

References 21 publications

A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

A Novel QP-Based Kinematic Redundancy Resolution Method With Joint Constraints Satisfaction

An Output Probabilistic Constrained Optimal Control Algorithm Based on Multivariable MAC and its Application in Looper Control System

Flexibility in Hexapod Robots: Exploring Mobility of the Body

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