Abstract-Controlling the robot with a permanently-updated optimal trajectory, also known as model predictive control, is the Holy Grail of whole-body motion generation. Before obtaining it, several challenges should be faced: computation cost, non-linear local minima, algorithm stability, etc. In this paper, we address the problem of applying the updated optimal control in real-time on the physical robot. In particular, we focus on the problems raised by the delays due to computation and by the differences between the real robot and the simulated model. Based on the optimal-control solver MuJoCo, we implemented a complete model-predictive controller and we applied it in real-time on the physical HRP-2 robot. It is the first time that such a whole-body model predictive controller is applied in real-time on a complex dynamic robot. Aside from the technical contributions cited above, the main contribution of this paper is to report the experimental results of this première implementation.

Research into legged robotics is primarily motivated by the prospects of building machines that are able to navigate in challenging and complex environments that are predominantly non-flat. In this context, control of contact forces is fundamental to ensure stable contacts and equilibrium of the robot. In this paper we propose a planning/control framework for quasi-static walking of quadrupedal robots, implemented for a demanding application in which regulation of ground reaction forces is crucial. Experimental results demonstrate that our 75-kg quadruped robot is able to walk inside two high-slope (50 • ) V-shaped walls; an achievement that to the authors' best knowledge has never been presented before. The robot distributes its weight among the stance legs so as to optimize user-defined criteria. We compute joint torques that result in no foot slippage, fulfillment of the unilateral constraints of the contact forces and minimization of the actuators effort. The presented study is an experimental validation of the effectiveness and robustness of QP-based force distributions methods for quasi-static locomotion on challenging terrain.

We present a contact planner for complex legged locomotion tasks: standing up, climbing stairs using a handrail, crossing rubble and getting out of a car. The need for such a planner was shown at the Darpa Robotics Challenge, where such behaviors could not be demonstrated (except for egress). Current planners suffer from their prohibitive algorithmic complexity, because they deploy a tree of robot configurations projected in contact with the environment. We tackle this issue by introducing a reduction property: the reachability condition. This condition defines a geometric approximation of the contact manifold, which is of low dimension, presents a Cartesian topology, and can be efficiently sampled and explored. The hard contact planning problem can then be decomposed into two sub-problems: first, we plan a path for the root without considering the whole-body configuration, using a sampling-based algorithm; then, we generate a discrete sequence of whole-body configurations in static equilibrium along this path, using a deterministic contact-selection algorithm. The reduction breaks the algorithm complexity encountered in previous works, resulting in the first interactive implementation of a contact planner (open source). While no contact planner has yet been proposed with theoretical completeness, we empirically show the interest of our framework: in a few seconds, with high success rates, we generate complex contact plans for various scenarios and two robots, HRP-2 and HyQ. These plans are validated either in dynamic simulations, or on the real HRP-2 robot.

This paper details the implementation of state-of-the-art whole-body control algorithms on the humanoid robot iCub. We regulate the forces between the robot and its surrounding environment to stabilize a desired posture. We assume that the forces and torques are exerted on rigid contacts. The validity of this assumption is guaranteed by constraining the contact forces and torques, e.g., the contact forces must belong to the associated friction cones. The implementation of this control strategy requires the estimation of both joint torques and external forces acting on the robot. We then detail algorithms to obtain these estimates when using a robot with an iCub-like sensor set, i.e., distributed six-axis force-torque sensors and whole-body tactile sensors. A general theory for identifying the robot inertial parameters is also presented. From an actuation standpoint, we show how to implement a joint-torque control in the case of DC brushless motors. In addition, the coupling mechanism of the iCub torso is investigated. The soundness of the entire control architecture is validated in a real scenario involving the robot iCub balancing and making contact with both arms.

Abstract-The upcoming generation of humanoid robots will have to be equipped with state-of-the-art technical features along with high industrial quality, but they should also offer the prospect of effective physical human interaction. In this paper we introduce a new humanoid robot capable of interacting with a human environment and targeting industrial applications. Limitations are outlined and used together with the feedback from the DARPA Robotics Challenge, and other teams leading the field in creating new humanoid robots. The resulting robot is able to handle weights of 6 kg with an out-stretched arm, and has powerful motors to carry out fast movements. Its kinematics have been specially designed for screwing and drilling motions. In order to make interaction with human operators possible, this robot is equipped with torque sensors to measure joint effort and high resolution encoders to measure both motor and joint positions.The humanoid robotics field has reached a stage where robustness and repeatability is the next watershed. We believe that this robot has the potential to become a powerful tool for the research community to successfully navigate this turning point, as the humanoid robot HRP-2 was in its own time.

This paper deals with the problem of controlling a robotic system whose joints have bounded position, velocity and acceleration/torque. Assuming a discrete-time acceleration control, we compute tight bounds on the current joint accelerations that ensure the existence of a feasible trajectory in the future. Despite the clear practical importance of this issue, no complete and exact solution has been proposed yet, and all existing control architectures rely on hand-tuned heuristics. We also extend this methodology to torque-controlled robots, for which joint accelerations are only indirectly bounded by the torque limits. Numerical simulations are presented to validate the proposed method, which is computationally efficient and hence suitable for high-frequency control.

Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing † .

Maintaining equilibrium is of primary importance for legged systems. It is not surprising then that static equilibrium is at the core of most control/planning algorithms for legged robots. Being able to check whether a system is in static equilibrium is thus important, and doing it efficiently is crucial. While this is straightforward for a system in contact with a flat ground only, it is not the case for arbitrary contact geometries. In this paper we propose two new techniques to test static equilibrium and we show that they are computationally faster than all other existing methods. Moreover, we address the issue of robustness to errors in the contact-force tracking, which could lead to slippage or rotation at the contacts. We extend all the discussed techniques to test for robust static equilibrium, that is the ability to maintain equilibrium while avoiding to lose contacts despite bounded force-tracking errors. Accounting for robustness does not affect the computation time of the equilibrium tests, while it qualitatively improves the contact postures generated by our reachability-based multicontact planner.