An Intuitive Formulation of the Human Arm Active Endpoint Stiffness

Optimal configurations for stiffness and compliance in human & robot arms

Research in neurophysiology has shown that humans are able to adapt the mechanical stiffness at the hand in order to resist disturbances. This has served as inspiration for optimising stiffness in robot arms during manipulation tasks. Endpoint stiffness is modelled in Cartesian space, as though the hand were in independent rigid body. But an arm is a series of rigid bodies connected by articulated joints. The contribution of the joints and arm configuration to the endpoint stiffness has not yet been quantified. In this paper we use mathematical optimisation to find conditions for maximum stiffness and compliance with respect to an externally applied force. By doing so, we can retroactively explain observations made about humans using these mathematically optimal conditions. We then show how this optimisation can be applied to robotic task planning and control. Experiments on a humanoid robot show similar arm posture to that observed in humans. This suggests there is an underlying physical principle by which humans optimise stiffness. We can use this to derive natural control methods for robots.

Elbow Joint Stiffness Functional Scales Based on Hill's Muscle Model and Genetic Optimization

The ultimate goal of rehabilitation engineering is to provide objective assessment tools for the level of injury and/or the degree of neurorehabilitation recovery based on a combination of different sensing technologies that enable the monitoring of relevant measurable variables, as well as the assessment of non-measurable variables (such as muscle effort/force and joint mechanical stiffness). This paper aims to present a feasibility study for a general assessment methodology for subject-specific non-measurable elbow model parameter prediction and elbow joint stiffness estimation. Ten participants without sensorimotor disorders performed a modified "Reach and retrieve" task of the Wolf Motor Function Test while electromyography (EMG) data of an antagonistic muscle pair (the triceps brachii long head and biceps brachii long head muscle) and elbow angle were simultaneously acquired. A complete list of the Hill's muscle model and passive joint structure model parameters was generated using a genetic algorithm (GA) on the acquired training dataset with a maximum deviation of 6.1% of the full elbow angle range values during the modified task 8 of the Wolf Motor Function Test, and it was also verified using two experimental test scenarios (a task tempo variation scenario and a load variation scenario with a maximum deviation of 8.1%). The recursive least square (RLS) algorithm was used to estimate elbow joint stiffness (Stiffness) based on the estimated joint torque and the estimated elbow angle. Finally, novel Stiffness scales (general patterns) for upper limb functional assessment in the two performed test scenarios were proposed. The stiffness scales showed an exponentially increasing trend with increasing movement tempo, as well as with increasing weights. The obtained general Stiffness patterns from the group of participants without sensorimotor disorders could significantly contribute to the further monitoring of motor recovery in patients with sensorimotor disorders.

Variable stiffness locomotion with guaranteed stability for quadruped robots traversing uneven terrains

Quadruped robots are widely applied in real-world environments where they have to face the challenges of walking on unknown rough terrains. This paper presents a control pipeline that generates robust and compliant legged locomotion for torque-controlled quadruped robots on uneven terrains. The Cartesian motion planner is designed to be reactive to unexpected early and late contacts using the estimated contact forces. Moreover, we present a novel scheme of optimal stiffness modulation that aims to coordinate desired compliance and tracking performance. It optimizes joint stiffness and contact forces coordinately in a quadratic programming (QP) formulation, where the constraints of non-slipping contacts and torque limits are imposed as well. In addition, the issue of stability under variable stiffness control is solved by imposing a tank-based passivity constraint explicitly. We finally validate the proposed control pipeline on our quadruped robot CENTAURO in experiments on uneven terrains and, through comparative tests, demonstrate the improvements of the variable stiffness locomotion.