Trajectory generation for multi-contact momentum-control

Simplified models of the dynamics such as the linear inverted pendulum model (LIPM) have proven to perform well for biped walking on flat ground. However, for more complex tasks the assumptions of these models can become limiting. For example, the LIPM does not allow for the control of contact forces independently, is limited to co-planar contacts and assumes that the angular momentum is zero. In this paper, we propose to use the full momentum equations of a humanoid robot in a trajectory optimization framework to plan its center of mass, linear and angular momentum trajectories. The model also allows for planning desired contact forces for each end-effector in arbitrary contact locations. We extend our previous results on LQR design for momentum control by computing the (linearized) optimal momentum feedback law in a receding horizon fashion. The resulting desired momentum and the associated feedback law are then used in a hierarchical whole body control approach. Simulation experiments show that the approach is computationally fast and is able to generate plans for locomotion on complex terrains while demonstrating good tracking performance for the full humanoid control

Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

A preliminary case study of the effect of shoe-wearing on the biomechanics of a horse’s foot

Horse racing is a multi-billion-dollar industry that has raised welfare concerns due to injured and euthanized animals. Whilst the cause of musculoskeletal injuries that lead to horse morbidity and mortality is multifactorial, pre-existing pathologies, increased speeds and substrate of the racecourse are likely contributors to foot disease. Horse hooves have the ability to naturally deform during locomotion and dissipate locomotor stresses, yet farriery approaches are utilised to increase performance and protect hooves from wear. Previous studies have assessed the effect of different shoe designs on locomotor performance; however, no biomechanical study has hitherto measured the effect of horseshoes on the stresses of the foot skeleton in vivo. This preliminary study introduces a novel methodology combining three-dimensional data from biplanar radiography with inverse dynamics methods and finite element analysis (FEA) to evaluate the effect of a stainless steel shoe on the function of a Thoroughbred horse's forefoot during walking. Our preliminary results suggest that the stainless steel shoe shifts craniocaudal, mediolateral and vertical GRFs at mid-stance. We document a similar pattern of flexion-extension in the PIP (pastern) and DIP (coffin) joints between the unshod and shod conditions, with slight variation in rotation angles throughout the stance phase. For both conditions, the PIP and DIP joints begin in a flexed posture and extend over the entire stance phase. At mid-stance, small differences in joint angle are observed in the PIP joint, with the shod condition being more extended than the unshod horse, whereas the DIP joint is extended more in the unshod than the shod condition. We also document that the DIP joint extends more than the PIP after midstance and until the end of the stance in both conditions. Our FEA analysis, conducted solely on the bones, shows increased von Mises and Maximum principal stresses on the forefoot phalanges in the shod condition at mid-stance, consistent with the tentative conclusion that a steel shoe might increase mechanical loading. However, because of our limited sample size none of these apparent differences have been tested for statistical significance. Our preliminary study illustrates how the shoe may influence the dynamics and mechanics of a Thoroughbred horse's forefoot during slow walking, but more research is needed to quantify the effect of the shoe on the equine forefoot during the whole stance phase, at faster speeds/gaits and with more individuals as well as with a similar focus on the hind feet. We anticipate that our preliminary analysis using advanced methodological approaches will pave the way for new directions in research on the form/function relationship of the equine foot, with the ultimate goal to minimise foot injuries and improve animal health and welfare

A hyper-redundant manipulator

“Hyper-redundant” manipulators have a very large number of actuatable degrees of freedom. The benefits of hyper-redundant robots include the ability to avoid obstacles, increased robustness with respect to mechanical failure, and the ability to perform new forms of robot locomotion and grasping. The authors examine hyper-redundant manipulator design criteria and the physical implementation of one particular design: a variable geometry truss