Nicolas Mansard

A versatile and efficient pattern generator for generalized legged locomotion

This paper presents a generic and efficient approach to generate dynamically consistent motions for under-actuated systems like humanoid or quadruped robots. The main contribution is a walking pattern generator, able to compute a stable trajectory of the center of mass of the robot along with the angular momentum, for any given configuration of contacts (e.g. on uneven, sloppy or slippery terrain, or with closed-gripper). Unlike existing methods, our solver is fast enough to be applied as a model-predictive controller. We then integrate this pattern generator in a complete framework: an acyclic contact planner is first used to automatically compute the contact sequence from a 3D model of the environment and a desired final posture; a stable walking pattern is then computed by the proposed solver; a dynamically-stable whole-body trajectory is finally obtained using a second-order hierarchical inverse kinematics. The implementation of the whole pipeline is fast enough to plan a step while the previous one is executed. The interest of the method is demonstrated by real experiments on the HRP-2 robot, by performing long-step walking and climbing a staircase with handrail support.

Fast algorithms to test robust static equilibrium for legged robots

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.

Optimal control for whole-body motion generation using center-of-mass dynamics for predefined multi-contact configurations

Multi-contact motion generation is an important problem in humanoid robotics because it generalizes bipedal locomotion and thus expands the functional range of humanoid robots. In this paper, we propose a complete solution to compute a fully-dynamic multi-contact motion of a humanoid robot. We decompose the motion generation by computing first a dynamically-consistent trajectory of the center of mass of the robot and finding then the whole-body movement following this trajectory. A simplified dynamic model of the humanoid is used to find optimal contact forces as well as a kinematic feasible center-of-mass trajectory from a predefined series of contacts. We demonstrate the capabilities of the approach by making the real humanoid robot platform HRP-2 climb stairs with the use of a handrail. The experimental study also shows that utilization of the handrail lowers the power consumption of the robot by 25% compared to a motion, where only the feet are used.

Whole-body motion integrating the capture point in the operational space inverse dynamics control

It is important for a humanoid robot to be able to move its body without falling down even if the target motion takes its center of mass to the limits of the support polygon. Usually the center of mass is overconstrained to keep balance, but this can make fast motion of the robot upper body or tasks that are far away from the reachable space unfeasible. To achieve these tasks that challenge the robot balance, this paper proposes the integration of the capture point (CP) in the operational-space inverse dynamics control framework. Then, if balance is about to be lost, a good place to step to will be determined preventing the robot from falling down. Moreover, the control of the CP as a task (or constraint) guarantees that it is kept within certain limits, allowing the foot to have time to safely step to it before the robot falls. An advantage over other methods is the transparent integration of the CP letting the robot be able to simultaneously move its whole body satisfying other tasks. The method has been tested in simulation using the dynamic model of HRP-2.

Trajectory generation for quadrotor based systems using numerical optimal control

The recent work on quadrotor have focused on more and more challenging tasks with increasingly complex systems. Systems are often augmented with slung loads, inverted pendulums or arms, and accomplish complex tasks such as going through a window, grasping, throwing and catching. Usually, controllers are designed to accomplish a specific task on a specific system using analytic solutions, so each application needs long preparations. On the other hand, the direct multiple shooting approach is able to solve complex problems without any analytic development, by using off-the-shelf optimization solver. In this paper, we show that this approach is able to solve a wide range of problems relevant to quadrotor systems, from on-line trajectory generation for quadrotors to going through a window for a quadrotor-and-pendulum system, through manipulation tasks for a aerial manipulator.

HPP: A new software for constrained motion planning

We present HPP, a software designed for complex classes of motion planning problems, such as navigation among movable objects, manipulation, contact-rich multiped locomotion, or elastic rods in cluttered environments. HPP is an open-source answer to the lack of a standard framework for these important issues for robotics and graphics communities.

Prioritized optimal control: A hierarchical differential dynamic programming approach

This paper deals with the generation of motion for complex dynamical systems (such as humanoid robots) to achieve several concurrent objectives. Hierarchy of tasks and optimal control are two frameworks commonly used to this aim. The first one specifies control objectives as a number of quadratic functions to be minimized under strict priorities. The second one minimizes an arbitrary user-defined function of the future state of the system, thus considering its evolution in time. Our recent work on prioritized optimal control merges the advantages of both these methods. This paper reformulates the original prioritized optimal control algorithm with the precise goal of improving its computational speed. We extend the dynamic programming method to work with a hierarchy of tasks. We compared our approach in simulation with both our previous algorithm and classical optimal control. The measured computational improvement represents another step towards the application of prioritized optimal control for online model predictive control of humanoid robots. We believe that this could be the key to unlock the (so far unexploited) dynamic capabilities of these mechanical systems.

A simulation framework for simultaneous design and control of passivity based walkers

In this paper, we propose a simulation framework which simultaneously computes both the design and the control of bipedal walkers. The problem of computing a design and a control is formulated as a single large-scale parametric optimal control problem on hybrid dynamics with path constraints (e.g. non sliding and non slipping contact constraints). Our framework relies on state-of-the-art numerical optimal control techniques and efficient computation of the multi-body rigid dynamics. It allows to compute both the parametrized model and the control of passive walkers on different scenarios, in only few seconds on a standard computer. The framework is illustrated by several examples which highlight the interest of the approach.

Humanoid robot task recognition from movement analysis

In this paper, we present a method to perform tasks identification on a humanoid robot. The observed motion is compared to a set of candidate controllers that the robot might be executing. The more relevant candidate controllers are selected, and can be used as a description of the motion, or as a basis to replicate a similar motion on another robot. The analysis of the movements is based on the task-function approach and is applied in the context of humanoid robot motions. A pool of tasks is defined in order to cover the range of possible motion of the robot and the demonstration movement is projected in each candidate task of that pool. The reduced trajectory is then compared with the characteristic task trajectory using a numerical optimization process. The movement is then projected into the null space of the best task candidate. As a consequence, the motion due to the task candidate is subtracted from the original movement. This process is iterated until the result of a projection becomes null. The approach is applied to recognize the tasks performed by a HRP-2 robot in simulation, in order to disambiguate very similar-looking motions. Preliminary directions are given for possible application for human motion recognition.

A kinematics-dynamics based estimator of the center of mass position for anthropomorphic system — A complementary filtering approach

This paper presents an original approach to simply and efficiently estimate the center of mass position of a free-floating base system, like a humanoid robot or a human body. This approach relies on the theory of complementary filtering, which is a popular technique in aerial robotics, but rarely implemented in humanoid robotics. The main idea consists in merging input measurements like the zero-moment point position, the contact forces, etc. which are then filtered according to their reliability in their respective spectral bandwidth. We validate this approach in simulation by (i) comparing the estimated center of mass trajectory with its real value and (ii) showing that the complementary filter offers on average a least reconstruction error than the classic Kalman filter.