Online Optimal Impedance Planning for Legged Robots

Abstract

Real world applications require robots to operate in unstructured environments. This kind of scenarios may lead to unexpected environmental contacts or undesired interactions, which may harm people or impair the robot. Adjusting the behavior of the system through impedance control techniques is an effective solution to these problems. However, selecting an adequate impedance is not a straightforward process. Normally, robot users manually tune the controller gains with trial and error methods. This approach is generally slow and requires practice. Moreover, complex tasks may require different impedance during different phases of the task. This paper introduces an optimization algorithm for online planning of the Cartesian robot impedance to adapt to changes in the task, robot configuration, expected disturbances, external environment and desired performance, without employing any direct force measurements. We provide an analytical solution leveraging the mass-spring-damper behavior that is conferred to the robot body by the Cartesian impedance controller. Stability during gains variation is also guaranteed. The effectiveness of the method is experimentally validated on the quadrupedal robot ANYmal. The variable impedance helps the robot to tackle challenging scenarios like walking on rough terrain and colliding with an obstacle.

Enhancing Robot-Environment Physical Interaction via Optimal Impedance Profiles

“…This implementation provides a coordinated, coherent and independent planning of robot dynamic behavior in Cartesian space, in terms of apparent stiffness and damping, together with the end-effector desired trajectory. Although it is common to impose a relationship between stiffness and damping, for instance to get critically damped systems (see [19] among others), in this work we decided to optimise the three parameters independently. In this way, the optimal solution was free to implement under-damped or over-damped conditions in specific portions of the motion, for example to increase velocity.…”

“…Adaptive impedance control has been used to account for differences between model and manipulator parameters [15], [16]. In addition, the ability to adapt controller parameters may be used to improve system performance and has been proposed to optimize task efficiency [17], [18], [19].…”

An Optimization-Based Locomotion Controller for Quadruped Robots Leveraging Cartesian Impedance Control

“…On the other hand, by assigning Λ d = Λ c , the impedance gains of Equation (10) can still be tuned by analytical techniques based on different configurations (see in Angelini et al, 2019 ), whereas HQP controllers rely on manual trial and error tuning.…”

Fractional Order Impedance Control

“…Traditional position servo control is with high gain (stiffness) and usually in kinematic control, which makes the robots rigid and increases the contact force. A good solution to deal with the impact is making the end-effector of robots work like a spring-damper [2], while the stiffness and damping should be variable with respect to time, terrains and tasks [3], [4].…”