Jae-Yun Jun

Dynamic stability of variable stiffness running

Humans and animals adapt their leg impedance during running for both internal(e.g. loading) and external(e.g. surface) changes. In this paper we examine the relationship between leg stiffness and the speed and stability of dynamic legged locomotion. We utilize a torque-driven reduced-order model of running based on a successful family of running robots to show how optimal clock-driven controllers can interact with variably compliant limbs to adapt to changing operating conditions. We show that the leg stiffness adaptation gives, in general, better results than simply optimizing the gait controller and nearly as good as the co-optimization of controller and leg stiffness.

Effect of rolling on running performance

The present work investigates the effect of rolling contact during stance phase in running by relating the variation of foot curvature radii to running efficiency, stability and forward speed. Both a conservative reduced-order running model and one with a simple motor and friction model are used to simulate running with a rolling foot. We find that having a larger foot radius implies smoother peak vertical ground reaction forces. Increased foot radius also yields, up to a point, a larger region of stable gaits for the conservative system, and more stable, fast, and efficient gaits for the actuated version. These results motivate the design of a new set of legs to test these findings on a dynamic running platform.

A reduced-order dynamical model for running with curved legs

Some of the unique properties associated with running with curved legs or feet (as opposed to point-contact feet) are examined in this work, including the rolling contact motion, the change of the legs effective stiffness and rest length, the shift of the effective flexion point along the leg, and the compliant-vaulting motions over its tiptoe during stance. To examine these factors, a novel torque-driven reduced-order dynamical model with a clock-based control scheme and with a simple motor model is developed (named as torque-driven and damped half-circle-leg model (TD-HCL)). The controller parameters are optimized for running efficiency and forward speed using a direct search method, and the results are compared to those of other existing dynamical models such as the torque-driven and damped spring-loaded-inverted-pendulum (TD-SLIP) model, the torque-driven and damped two-segment-leg (TD-TSL) model, and the TD-SLIP with a rolling foot (TD-SLIP-RF) model. The results show that running with rolling is more efficient and more stable than running with legs that involve pin joint contact model. This work begins to explain why autonomous robots using curved legs run efficiently and robustly. New curved legs are designed and manufactured in order to validate these results.

Pose estimation-based path planning for a tracked mobile robot traversing uneven terrains

A novel path-planning algorithm is proposed for a tracked mobile robot to traverse uneven terrains, which can efficiently search for stability sub-optimal paths. This algorithm consists of combining two RRT-like algorithms (the Transition-based RRT (T-RRT) and the Dynamic-Domain RRT (DD-RRT) algorithms) bidirectionally and of representing the robot-terrain interaction with the robots quasi-static tip-over stability measure (assuming that the robot traverses uneven terrains at low speed for safety). The robots stability is computed by first estimating the robots pose, which in turn is interpreted as a contact problem, formulated as a linear complementarity problem (LCP), and solved using the Lemkes method (which guarantees a fast convergence). The present work compares the performance of the proposed algorithm to other RRT-like algorithms (in terms of planning time, rate of success in finding solutions and the associated cost values) over various uneven terrains and shows that the proposed algorithm can be advantageous over its counterparts in various aspects of the planning performance. Robot pose and its stability are estimated to plan paths over uneven terrains.The path-planning problem over uneven terrains is solved using a novel algorithm.More stable paths can be found with the novel approach than with other approaches.The planning is tested over a real 3D point-cloud map built with a 3D RGB sensor.

Compliant Leg Shape, Reduced-Order Models and Dynamic Running

The groundbreaking running performances of RHex-like robots are analyzed from the perspective of their leg designs. In particular, two-segment-leg models are used both for studying the running with the legs currently employed and for suggesting new leg designs that could improve the gait stability, running efficiency and forward speed. New curved compliant monolithic legs are fabricated from these models, and the running with these legs is tested by using a newly designed running test robot. Both the simulations and the experimental trials seem to suggest that running with legs with unity-ratio of the leg segments is faster and more efficient than running with the leg that is currently used on the RHex-like robots. The simulation model predictions seem to match closely to experimental trials in some instances but not always. In the future, a more sophisticated model is needed to capture the actual running with curved legs more accurately.

A trajectory tracking control design for a skid-steering mobile robot by adapting its desired instantaneous center of rotation

A skid-steering mobile robot steers by creating a moment that is larger than the frictional moment which results in a lateral slippage also known as skidding. This moment is in turn generated by a difference of the forces originated from the two sides of the robot. Tracking a given trajectory using this type of steering mechanism is not easy since it requires to relate skidding to steering. A necessary condition for the stability of skid-steering mobile robots is that the longitudinal component of the instantaneous center of rotation (ICR) resides within the robot dimension. In the present work, we propose a novel trajectory-tracking control design using a backstepping technique that guarantees the Lyapunov stability and that satisfies this necessary condition by relating the longitudinal component of the “desired ICR” to the curvature of a given trajectory and the reference linear speed. Finally, we compare the performance of the proposed controller to that of other existing controllers for skid-steering mobile robots and show the robustness of the proposed controller even in the presence of modeled sensory noise and control time delay in simulation.

Characterization of running with compliant curved legs

Running with compliant curved legs involves the progression of the center of pressure, the changes of both the legs stiffness and effective rest length, and the shift of the location of the maximum stress point along the leg. These phenomena are product of the geometric and material properties of these legs, and the rolling motion produced during stance. We examine these aspects with several reduced-order dynamical models to relate the legs design parameters (such as normalized foot radius, legs effective stiffness, location of the maximum stress point and leg shape) to running performance (such as robustness and efficiency). By using these models, we show that running with compliant curved legs can be more efficient, robust with fast recovery behavior from perturbations than running with compliant straight legs. Moreover, the running performance can be further improved by tuning these design parameters in the context of running with rolling. The results shown in this work may serve as potential guidance for future compliant curved leg designs that may further improve the running performance.

Forecasting Negative Yield-Curve Distributions

Negative interest rates are present in various marketplaces since mid-2014, following the negative interest rate policy (NIRP) adopted by the European Central Bank in order to lift the economic growth (and, therefore, the inflation). However, this policy involves difficulties for market practitioners as there is no model that enables to forecast negative interest rates in a coherent and sounding theoretical manner. Facing this lack of reliable models, the well-known Historical Approach (HA) appears to be a good resource. By tweaking the HA, we derive a data-driven and very tractable tool that allows practitioners to generate yield-curve distribution at future discrete time horizons. So, we provide a robust and easy-to-understand forecasting model, suitable for the NIRP context, allowing to appreciate its prediction power. Besides the methodology development that we present in this work, various numerical illustrations are reported in order to shed light on the benefit (and the limit) of our forecasting approach.

Stability-based planning and trajectory tracking of a mobile manipulator over uneven terrains

The problem of improving the stability of a mobile manipulator over a sloped terrain is addressed in the present work. Such an improvement is achieved by finding the location of the manipulators center of mass that maximizes the overall quasi-static stability, defined here as the force-angle stability, using a stochastic optimization approach known as the Covariance Matrix Adaptation. The tracking of both trajectories for the robot base and for the manipulator is achieved by using an inverse-kinematics controller in simulation.

TIP-OVER STABILITY-BASED PATH PLANNING FOR A TRACKED MOBILE ROBOT OVER ROUGH TERRAINS

Most of the existing path planners for traversing over rough terrains use the single-valued probabilistic properties of the terrain with the extension of considering the robot’s dimensions to build the cost function. The present work proposes a path planner for a tracked mobile robot to traverse over rough terrains using the robot’s tip-over stability as its cost function. The contacts that the robot makes with the terrain determine the pose of the robot and in turn its tip-over stability. The estimation of the robot’s pose is formulated as a linear complementary problem (LCP) and solved using the Lemke’s method. We show some examples on searching paths that optimize for various cost functions over a randomly generated rough terrain. We also validate the performance of our pose estimator by comparing their results to those obtained from a dynamic simulator (MSC Adams).