This article proposes an invariant smoother for legged robot state estimation with the measurement of an inertial measurement unit and leg kinematics while assuming static foot contact. Because the proposed smoother is formulated with the residual functions with group-affine property, their Jacobians become independent from current state estimates. These state-independent Jacobians lead to better convergence properties in optimizing the cost in the smoother, especially under dynamic contact events. The proposedslip rejectionmethod increases the uncertainty of static contact assumption when the robot has dynamic contact events. The estimated foot velocity, which is utilized to detect the dynamic contact events, is re-evaluated within the preserving time window. We also propose thecontact loopmethod, a new measurement model asserting that foot position remains constant over multiple timesteps during stable contact. The proposed estimator is tested through online experiments, including indoor and 160 m-long outdoor experiments, and compared against state-of-the-art algorithms.

In this work, a non-gaited framework for legged system locomotion is presented. The approach decouples the gait sequence optimization by considering the problem as a decision-making process. The redefined contact sequence problem is solved by utilizing a Monte Carlo Tree Search (MCTS) algorithm that exploits optimization-based simulations to evaluate the best search direction. The proposed scheme has proven to have a good trade-off between exploration and exploitation of the search space compared to the state-of-the-art Mixed-Integer Quadratic Programming (MIQP). The model predictive control (MPC) utilizes the gait generated by the MCTS to optimize the ground reaction forces and future footholds position. The simulation results, performed on a quadruped robot, showed that the proposed framework could generate known periodic gait and adapt the contact sequence to the encountered conditions, including external forces and terrain with unknown and variable properties. When tested on robots with different layouts, the system has also shown its reliability.

This paper introduces a design method for an efficient and agile quadruped robot. A mixed-integer optimization formulation including the number of gear teeth is derived to obtain the optimal gear ratio that minimizes cost for a running-trot with the target speed of 3 m/s. With the inclusion of integer constraints related to the number of gear teeth, detailed design considerations of gear trains can be included in the optimization process. Thermal dissipation of the motor controller is also taken into account in the optimization to consider heat generation during high-speed running. KAIST Hound, a 45 kg robot, designed with the obtained design parameters has successfully demonstrated a 3 m/s running-trot using a nonlinear model predictive controller (NMPC). Furthermore, the robot has proved its robustness by the demonstration of additional experiments such as 22° slope climbing, 3.2 km walking, and traversing a 35 cm obstacle.

In this work, we propose a novel differential dynamic programming (DDP) framework for systems involving contact with the ground. The approach converts a general constrained differential dynamic programming into contact-implicit one by incorporating contact dynamics in a linear complementarity problem (LCP) formulation. Analytical gradients of the contact dynamics are obtained through a relaxed complementarity condition in the LCP formulation that helps the search directions of optimization avoid stalling in bad local minima or saddle points. Incorporation of contact dynamics and its analytical gradients into DDP enables an online discovery of not only dynamically-feasible trajectories of states, control inputs, and contact forces but also contact mode sequences. We demonstrate that our Contact-Implicit Differential Dynamic Programming framework successfully finds totally new dynamic motions with contact mode sequences in a variety of robotic systems including an one-legged hopping robot and planar quadrupedal robot in simulation environment.

This paper presents a reduction mechanism for robot actuators that can switch between two types of reduction ratio. By fixing the carrier or ring gear of the proposed actuator which is based on the 3K compound planetary drive, the actuator can shift its reduction ratio. For compact design with reduced weight of the actuator, unique pawl brake mechanism interacting with cams and micro servos for switching mechanism is designed. The resulting prototype module has a reduction ratio of 6.91 and 44.93 for ‘low-reduction’ and ‘high-reduction’ ratios, respectively. Reduction ratios can be easily adjusted by modifying the pitch diameters of gears. Experimental results demonstrate that the proposed actuator could extend its operation region via two reduction modes that are interchangeable with gear shifting.

This paper presents a constrained nonlinear model predictive control (NMPC) framework for legged locomotion. The framework assumes a legged robot as a floating base single rigid body with contact forces being applied to the body as external forces. With consideration of orientation dynamics evolving on the rotation manifold SO(3), analytic Jacobians which are necessary for constructing the gradient and the Gauss-Newton Hessian approximation of the objective function are derived. This procedure also includes the reparameterization of the robot orientation on SO(3) to orientation error in the tangent space of that manifold. Obtained gradient and Gauss-Newton Hessian approximation are utilized to solve nonlinear least squares problems formulated from NMPC in a computationally efficient manner. The proposed algorithm is verified on various types of legged robots and gaits in a simulation environment.

This paper introduces an obstacle-avoiding algorithm for bipedal robots, especially in push recovery situations. Typically, There are many algorithms that plan footstep to avoid obstacles based on vision recognition data. However, if the robot is pushed, the planned footprint will change, and thus, there is no guarantee that it will avoid obstacles. Although modified stepping positions can be limited, the robot's stability is not assured. Our proposed algorithm focuses on avoiding obstacles through vision recognition in push recovery situations and generating compensation actions for instability by restricting modified footsteps. We fuse vision feedback with our previous push recovery algorithm, which optimizes the ankle, hip, and stepping strategies. We build simple grid data using vision recognition and apply it to the inequality constraint of the stepping position. We validate the effectiveness of our algorithm using the bipedal platform GAZELLE with the Kinect V2 RGBD sensor.