Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these challenges, we focus on polynomial systems and propose the Max Entropy Moment Kalman Filter (MEM-KF). To address 1), we represent arbitrary beliefs by a Moment-Constrained Max-Entropy Distribution (MED). The MED can asymptotically approximate almost any distribution given an increasing number of moment constraints. To address 2), we model the noise in the process and observation model as MED. To address 3), we propagate the moments through the process model and recover the distribution as MED, thus avoiding symbolic integration, which is generally intractable. All the steps in MEM-KF, including the extraction of a point estimate, can be solved via convex optimization. We showcase the MEM-KF in challenging robotics tasks, such as localization with unknown data association.

This paper develops a novel slip estimator using the invariant observer design theory and Disturbance Observer (DOB). The proposed state estimator for mobile robots is fully proprioceptive and combines data from an inertial measurement unit and body velocity within a Right Invariant Extended Kalman Filter (RI-EKF). By embedding the slip velocity into SE3(3) matrix Lie group, the developed DOB-based RI-EKF provides real-time velocity and slip velocity estimates on different terrains. Experimental results using a Husky wheeled robot confirm the mathematical derivations and effectiveness of the proposed method in estimating the observable state variables. Open-source software is available for download and reproducing the presented results.

This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra. Moreover, given an initial condition, the linearized tracking error dynamics and equations of motion are globally valid and evolve independently of the system trajectory. By exploiting the symmetry of the problem, the proposed approach shows faster convergence of rotation and position simultaneously than the state-of-the-art geometric variational MPC based on variational-based linearization. Numerical simulation on tracking control of a fully-actuated 3D rigid body dynamics confirms the benefits of the proposed approach compared to the baselines. Furthermore, the proposed MPC is also verified in pose control and locomotion experiments on a quadrupedal robot MIT Mini Cheetah.

This paper proposes a state estimator for legged robots operating in slippery environments. An Invariant Extended Kalman Filter (InEKF) is implemented to fuse inertial and velocity measurements from a tracking camera and leg kinematic constraints. The misalignment between the camera and the robot-frame is also modeled thus enabling auto-calibration of camera pose. The leg kinematics based velocity measurement is formulated as a right-invariant observation. Nonlinear observability analysis shows that other than the rotation around the gravity vector and the absolute position, all states are observable except for some singular cases. Discrete observability analysis demonstrates that our filter is consistent with the underlying nonlinear system. An online noise parameter tuning method is developed to adapt to the highly time-varying camera measurement noise. The proposed method is experimentally validated on a Cassie bipedal robot walking over slippery terrain. A video for the experiment can be found at https://youtu.be/VIqJL0cUr7s.