With the advancement of robot manipulator technologies, developing custom-made low-cost manipulator arms has gained increasing popularity in the field of robotics. However, these low-cost systems often lack precise sensing and control capabilities, making reliable collision detection particularly critical to ensure safe operation. Popular methods of collision detection, which estimate external disturbances such as generalized Momentum Observer (MO) critically rely on an accurate dynamics model, and precise system identification requires joint torque sensors that are expensive for low-cost manipulators. This paper presents a novel approach to improve collision detection for low-cost robot manipulators where modeling error is present and torque sensing is not available. We propose a probabilistic framework using Gaussian Mixture Models (GMM) to capture friction and other unmodeled dynamics of a robot manipulator. Instead of explicitly identifying model parameters, GMM is created on the total residual torque of the MO while running an excitation trajectory. The GMM is then deployed in the main control loop to identify external disturbances from the residual torque of the same momentum observer. The approach is validated on a custom-made 4-Degrees-of-Freedom (DoF) robot arm with modeling error, unmodeled dynamics, and with only joint position measurement. Our method achieves reliable detection on both hard and soft collisions, demonstrating a reduction in the false positive rate by more than 50% compared to conventional MO-based methods with the same true positive rate on the same hardware.

Motion planning techniques for quadrotors have advanced significantly over the past decade. Most successful planners have two stages: a front-end that determines a path that incorporates geometric (or kinematic or input) constraints and specifies the homotopy class of the trajectory, and a back-end that optimizes this path to respect dynamics and input constraints. While there are many different choices for each stage, the eventual performance depends critically not only on these choices, but also on the environment. Given a new environment, it is difficult to decide a priori how one should design a motion planner. In this work, we develop (i) a procedure to construct parametrized environments, (ii) metrics that characterize the difficulty of motion planning in these environments, and (iii) an open-source software stack that can be used to combine a wide variety of two-stage planners seamlessly. We perform experiments in simulations and a real platform. We find, somewhat conveniently, that geometric front-ends are sufficient for environments with varying complexities if combined with dynamics-aware backends. The metrics we designed faithfully capture the planning difficulty in a given environment. All code is available at https://github.com/KumarRobotics/kr_mp_design.

Performing real-time receding horizon motion planning for autonomous vehicles while providing safety guarantees remains difficult. This is because existing methods to accurately predict ego vehicle behavior under a chosen controller use online numerical integration that requires a fine time discretization and thereby adversely affects real-time performance. To address this limitation, several recent papers have proposed to apply offline reachability analysis to conservatively predict the behavior of the ego vehicle. Reachable sets can be constructed by utilizing a simplified model whose behavior is assumeda priorito conservatively bound the dynamics of a full-order model. However, it can be challenging to meticulously construct this conservative bound. This paper proposes a framework named REFINE to overcome the limitations of these existing approaches. REFINE utilizes a parameterized robust controller that partially linearizes the vehicle dynamics even in the presence of modeling error. Zonotope-based reachability analysis is then performed on the closed-loop, full-order vehicle dynamics to offline compute the corresponding control-parameterized, over-approximate Forward Reachable Sets (FRS). Because reachability analysis is applied to the full-order model, the potential conservativeness introduced by using a simplified model is avoided. The pre-computed, control-parameterized FRS is then used online in an optimization framework to ensure safety. The proposed method is compared to several state-of-the-art methods during a simulation-based evaluation on a full-size vehicle model and is demonstrated on a$\frac{1}{10}$th race car robot in real hardware testing. In contrast to existing methods, REFINE is shown to enable the vehicle to safely navigate itself through complex environments.