Efficient Computation of Interval-Arithmetic-Based Robust Controllers for Rigid Robots

Abstract

Abstract-We propose a method for efficient numerical computation of interval-arithmetic-based robust controllers for rigid robot manipulators. The use of interval arithmetic for robust control is the core of a recently proposed approach which allows a user-defined tracking performance to be ultimately met despite uncertain models and input disturbance, without requiring an empirical estimation of bounds of perturbations from uncertain system dynamics. Our proposed algorithm combines a modified recursive Newton-Euler scheme with interval arithmetic computations to automatically obtain formally guaranteed over-approximative estimations of perturbing torques/forces arising from imperfect knowledge of dynamic model parameters. The resulting algorithm has linear computational complexity and can be used online. We validate the applicability of our proposed method with simulations and tests on a commercially available real-time target computer.

Reachable Sets for Safe, Real-Time Manipulator Trajectory Design

“…These parameterized trajectories are functions only of time for each parameter k ∈ K. In addition, they specify the arm's kinematics, with no notion of dynamics. This is a common approach in motion planning [7]- [11], because existing controllers can track kinematic trajectories closely (e.g., within 0.01 rad for revolute joints [26], [27]) in the absence of disturbances such as collisions. We find these kinematic trajectories sufficient to ensure no collisions in real-world hardware demonstrations (Sec.…”

“…V). Also, note that methods exist for quantifying tracking error using zonotopes [27] and accounting for it at runtime [15]. The second property in the definition of the trajectory parameter leverages the fact that trajectories can evolve from q(0; k) = 0 without loss of generality, because q(•; k) does not depend on q.…”

Interval-Arithmetic-Based Trajectory Scaling and Collision Detection for Robots with Uncertain Dynamics

“…To generate an interval within which the commanded torque must lie, we propose the idea of extending the IANEA from [14] to incorporate an interval for joint accelerations and disturbance and modify it to better handle static friction. When estimating torques based on a trajectory, we face the problem of being unable to reliably measure joint accelerations.…”

“…The extension of the IANEA from [14] is straightforward, and every operation that involvesq q q becomes a set-based operation.…”

“…Furthermore, the required measurements for torque or acceleration are usually noisy or not available at all. We relax this assumption by employing a recent method proposed in [14]: The classical recursive Newton Euler algorithm is enhanced by using interval arithmetic and thus produces over-approximative sets of joint torques/forces that emerge from uncertainties in the dynamical parameters of the model. From now on we refer to this algorithm as the interval-arithmetic-based Newton-Euler algorithm (IANEA).…”