Provably-Safe, Online System Identification

TL;DR

The paper tackles safe online identification of end effector inertial parameters for robotic manipulators manipulating unknown payloads under environmental and actuator constraints. It fuses a provably-safe trajectory optimization approach based on ARMOUR with a robust interval arithmetic–driven system identification that yields overapproximate bounds $[\theta]$ guaranteed to contain the true $\theta_e$. Key contributions include a real time locally exciting trajectory generator that respects safety constraints, a momentum based regression framework with physical consistency enforced via log-Cholesky parameterization, and an end to end online identification pipeline with guaranteed safety during data collection. Hardware experiments on a Kinova gen3 demonstrate that the method achieves tighter parameter bounds and reliable task completion under significant inertial uncertainty, with open source code provided for reproducibility and benchmarking.

Abstract

Precise manipulation tasks require accurate knowledge of payload inertial parameters. Unfortunately, identifying these parameters for unknown payloads while ensuring that the robotic system satisfies its input and state constraints while avoiding collisions with the environment remains a significant challenge. This paper presents an integrated framework that enables robotic manipulators to safely and automatically identify payload parameters while maintaining operational safety guarantees. The framework consists of two synergistic components: an online trajectory planning and control framework that generates provably-safe exciting trajectories for system identification that can be tracked while respecting robot constraints and avoiding obstacles and a robust system identification method that computes rigorous overapproximative bounds on end-effector inertial parameters assuming bounded sensor noise. Experimental validation on a robotic manipulator performing challenging tasks with various unknown payloads demonstrates the framework's effectiveness in establishing accurate parameter bounds while maintaining safety throughout the identification process. The code is available at our project webpage: https://roahmlab.github.io/OnlineSafeSysID/.

Figures (12)

• Figure 1: This figure illustrates how the method proposed in this paper. (a) Initially, the 7 degree-of-freedom Kinova-gen3 robotic arm picks up a series of heavy dumbbells that are close to the design limit of the robot. The inertial parameters of this payload are unknown. (b) The robot then performs online system identification to estimate an interval bound using the method developed in this paper. The interval estimate of the inertial parameters generated by the algorithm is guaranteed to include the true inertial parameters of the dumbbell. Notably, the data used to compute this interval estimate is constructed in a manner that is guaranteed to be collision free while satisfying joint and torque limits. The inertial parameter bound is then used to update the planner and the controller, which allows the robot to (c) safely move all dumbbells to the other side around the obstacles and then (d) stack them vertically in order of increasing weight, which requires high precision. Our experiments illustrate that state-of-the-art methods that do not incorporate such provably overapproximative estimates of the inertial parameters result in a failure to complete the task safely, due to exceeding the torque limits, colliding with obstacles, or misplacing the dumbbells.
• Figure 2: This figure summarizes the proposed framework. Initially, the approach assumes an overapproximated bound on the inertial parameters of the robot end-effector with unknown payloads. A trajectory planner (Section \ref{['sec-06-trajopt']}) then generates a provably-safe, locally exciting desired trajectory in real-time based on this initial bound. A robust controller, modified from michaux2023cant, tracks this exciting trajectory while collecting robot data including joint positions, velocities, and applied torques. Using this collected data, the robust system identification method (Section \ref{['sec-05-sysid']}) generates a new, tighter overapproximated bound on the end-effector's inertial parameters. This process iterates continuously, with additional data enabling more precise parameter estimation and improved planner and controller performance.
• Figure 3: This figure illustrates a complex pick-and-place task used in the hardware experiment. Five dumbbells are placed on one side of the robot, whose inertial parameters are unknown to it (first image in both rows). The robot is required to move each dumbbell around the obstacles, place the lightest dumbbell on a 3D-printed platform in front of it, and stack the remaining dumbbells vertically in ascending order of weight (fourth image in both rows). We design two experiments with different settings: (a) The 3D-printed platform is positioned 0.25 m from the robot, with one low obstacle in the way, as shown in the images in the first row. (b) The 3D-printed platform is positioned 0.50 m from the robot, with one high obstacle in the way, as shown in the images in the second row.
• Figure 4: An illustration of the third real-world experiment. The robot is required to pick up and perform system identification with an 8lb dumbbell and then follow a trajectory to avoid obstacles.
• Figure 5: This figure illustrates the evolution of the estimated end-effector mass over time as the robot picks up and places the 4lb dumbbell in Experiment (b). For both "ours" and "random", we only plot the nominal estimate $\theta_{\text{\footnotesize{e}}, 0}$. For both "ours" and "adap-1-excit", an additional identification phase (from 4 to 11.5 seconds) is included, during which the robot tracks four exciting trajectories from Algorithm \ref{['alg:overall']} to identify the end-effector inertial parameters. In contrast, "random" follows four randomly generated trajectories during this phase instead of exciting ones. For "adap-1", since the identification phase is skipped entirely and the robot directly executes the task (i.e., moving and stacking the dumbbells onto the platform), the identification phase (4-11.5 second) is denoted as a dotted line. We observe that "ours" achieves more accurate estimation of the end-effector parameters than random", demonstrating the effectiveness of using exciting trajectories. Additionally, "adap-1-excit" benefits from both extended identification time and proper data excitation, resulting in improved estimation accuracy and thus, a higher success rate in the experiments compared to "adap-1".

Theorems & Definitions (16)

• Definition 1: Multidimensional Interval
• Definition 2: Interval Evaluation
• Theorem 5: Momentum-Based Dynamics paper-momentum
• Theorem 7: Standard Dynamics Regressor paper-linear-relationship
• Theorem 8: Momentum-Based Regressors paper-momentum and paper-CTq-regressor
• Definition 9: Measurement Data
• Corollary 10: Momentum-Based Parameter Identification
• Theorem 11: Uncertainty-Free System Identification
• proof
• Theorem 13