Adaptive Control of Motor-Position-Controlled Flexible Joint Robots with Uncertain Joint Stiffness
Authors: Annika Kirner, Grazia Zambella, Igor Kovacevic, Hannes Höppner, Jee-Hwan Ryu, Christian Ott
Abstract
Model-based control of flexible joint robots with position-controlled actuators relies on accurate knowledge of the joint compliance. In practice, precise stiffness models are often unavailable as the properties of physical elastic elements vary with operating conditions and slowly change over time due to wear and aging. To improve model-based control of these systems, we propose an adaptive control approach in this work, which updates an estimate of the uncertain, nonlinear torque-deflection relation of each joint. As opposed to classical adaptive control approaches for non-elastic robots, we rely on an implicit control law and a control-input-dependent regressor matrix to account for the uncertain joint stiffness. We analyze robustness of the approach against errors induced by the motor position controller. Experimental results on a flexible joint with nonlinear stiffness characteristics demonstrate the effectiveness of the proposed approach.
Robots working in unstructured or partially unobservable environments must combine accurate motion with physical compliance that can passively correct contact misalignment. Soft robots provide this compliance but have struggled to precisely control their tip compliance and position. This paper presents a robot architecture designed around that control problem: a 7-link arm whose six articulated joints provide twelve independently driven revolute axes, each actuated by an antagonistic pair of pneumatic muscles, so that every axis can simultaneously change its angle and linearly adjust its stiffness. The rigid articulated backbone makes the tip compliance and position of the arm predictable enough to be commanded quantitatively in real time. The robot employs a unified iterative inverse-kinematics and inverse-compliance controller to achieve simultaneous, quantitative control of both compliance and position. The task-space compliance and kinematics models and the control law are derived and verified on both the physical arm and a matched simulation. Simulation is then used to study how the same framework extends to other arm morphologies. Finally, the arm demonstrates tasks that have been difficult for both rigid and soft arms: rejecting disturbances while writing on a moving whiteboard, and passively correcting hidden misalignment during a key-insertion and drawer-opening task. That these tasks succeed under so straightforward a controller is evidence for the advantage of this algorithm-informed structural design.
This paper presents a subsystem-based adaptive control framework for serial flexible manipulators with an arbitrary number of links, in which the elastic deformation PDE of each link is carried through the entire control design without spatial discretization or modal truncation. All dynamic quantities -- rigid-body motion, elastic deformation, and inter-link constraint forces -- are expressed uniformly as body-fixed twists and wrenches within the se3 Lie-algebraic structure. A controllable form of the per-link dynamics is derived by substituting the strain-based deformation PDE into the dynamic equation, eliminating distributed elastic acceleration and yielding a model governed by the body-fixed twist acceleration and deformation field. Desired subsystem twist trajectories are generated via a deflection-compensating inverse kinematics procedure. A nominal per-link controller is proven to produce exponential twist error decay via a per-subsystem Lyapunov function. An adaptive modification replaces exact physical parameters with online estimates governed by a projection-based law, augmenting with a parameter estimation error term. Upon summing over all links, the interaction power terms telescope to zero by Newton's third law and the frame invariance of the natural power pairing on se3se(3), establishing exponential convergence of all twist errors and bounded elastic deformation under both nominal and adaptive controllers. The screw-theoretic structure renders interaction term cancellation exact, making the stability certificate modular and scalable to chains of arbitrary length. The framework is validated numerically on a two-link flexible manipulator in three-dimensional motion.
This paper proposes actuator-aware inverse kinematics for torque-controlled redundant robots under joint-limit constraints. In the considered architecture, the inverse-kinematic output is not merely a purely kinematic joint-velocity command; it is the required joint velocity supplied to a downstream torque-level controller. Therefore, a small commanded task residual may not necessarily improve realized motion. The proposed method formulates a convex quadratic programming problem whose decision variable is the joint-level required velocity. Control barrier function style bounds impose reference-level joint-limit admissibility, while the task equation is handled through a penalized slack variable. Redundancy is resolved using a controller-compatibility objective that accounts for previous-command consistency and actuator torque-capacity weighting. The method is independent of the particular torque-level controller and can serve as an intermediate IK layer between an endpoint trajectory and a redundant robot controller. Experiments on a virtual-decomposition-controlled seven-degree-of-freedom upper-limb exoskeleton compare the method with standard inverse-kinematic baselines and a constrained task-preserving quadratic programming baseline. The results indicate lower limit-pushing commands, bounded admissible required velocities, and improved realized task behavior in the tested trajectory, without modifying the downstream controller.