Geometrical postural optimisation of 7-DoF limb-like manipulators

Abstract

Robots are moving towards applications in less structured environments, but their model-based controllers are challenged by the tasks’ complexity and intrinsic environmental unpredictability. Studying biological motor control can provide insights into overcoming these limitations due to the high dexterity and stability observable in humans and animals. This work presents a geometrical solution to the postural optimisation of 7-DoF limbs-like mechanisms, which are robust to singularities and computationally efficient. The theoretical formulation identified two separate decoupled optimisation strategies. The shoulder and elbow strategy align the plane of motion with the expected plane of motion and guarantee the reachability of the end-posture. The wrist strategy ensures the end-effector orientation, which is essential to retain manipulability when nearing a singular configuration. The numerical results confirmed the theoretical observations and allowed us to identify the effect of different grasp strategies on system manipulability. The geometrical method was numerically tested in thousands of configurations proving to be both robust and accurate. The tested scenarios include left and right arm postures, singular configurations, and walking scenarios. The proposed geometrical approach can find application in developing efficient and robust interaction controllers that could be applied in computational neuroscience and robotics.

Harmonic Passive Motion Paradigm

“…The H-PMP is composed of a series of hierarchically semi-autonomous controllers and planner and a deterministic non-linear mapping for postural optimisation robust to singularities [5, 43]. The planners and controller are stable non-linear oscillators (i.e., fractal attractor) that can be tuned online, and are robust to delays and model uncertainties [4, 5, 9, 10, 42].…”

“…The arm postural optimisation and IK exploit a recently introduced geometrical solution, described by one of the functions of the motor cortex. We have chosen this approach because it generates a deterministic non-linear mapping robust to singularities between the task-space and the joint-space exploiting the kineto-static duality [43], and could be performed by the nervous system relying on an internal model present in the cerebellum. The definition of the optimal posture can be identified by aligning the arm plane of motion with the task dynamics, leading to manipulability properties equivalent to a planar 3-link arm [43].…”

“…However, using the proposed approach requires an architecture that relies on only the projection of efforts (force and torques) from the task to the joint space and, consequently, only the projection of kinematics from the joint to the task space. Additionally, it also requires the identifications of geometrical solutions that are designed ad hoc on the system mechanism [42, 43]. Essential to solving this problem is the FIC because it provides an algorithmic representation of a stable, conservative non-linear oscillator that can be online tuned to oscillate with a harmonic trajectory at the desired frequency and, consequently, control the movement velocity.…”