Sebastien Lengagne

Generation of whole-body optimal dynamic multi-contact motions

We propose a method to plan optimal whole-body dynamic motion in multi-contact non-gaited transitions. Using a B-spline time parameterization for the active joints, we turn the motion-planning problem into a semi-infinite programming formulation that is solved by nonlinear optimization techniques. Our main contribution lies in producing constraint-satisfaction guaranteed motions for any time grid. Indeed, we use Taylor series expansion to approximate the dynamic and kinematic models over fixed successive time intervals, and transform the problem (constraints and cost functions) into time polynomials which coefficients are function of the optimization variables. The evaluation of the constraints turns then into computation of extrema (over each time interval) that are given to the solver. We also account for collisions and self-collisions constraints that have not a closed-form expression over the time. We address the problem of the balance within the optimization problem and demonstrate that generating whole-body multi-contact dynamic motion for complex tasks is possible and can be tractable, although still time consuming. We discuss thoroughly the planning of a sitting motion with the HRP-2 humanoid robot and assess our method with several other complex scenarios.

Generation of dynamic motions under continuous constraints: Efficient computation using B-Splines and Taylor polynomials

This paper proposes a new computation method to solve semi-infinite optimization problems for motion planning of robotic systems. Usually, this problem is solved by means of time-grid discretization of the continuous constraints. Unfortunately, discretization may lead to unsafe motions since there is no guarantee of constraint satisfaction between time samples. First, we show that constraints such as joint position and velocity do not need time-discretization to be checked. Then, we present the computation method based on Taylor polynomials to evaluate more complex constraints over time-intervals. This method also applies to continuous equality constraints, to continuous maximum derivative constraint, and to compute the cost function.

Fmri-based robotic embodiment: Controlling a humanoid robot by thought using real-time fmri

We present a robotic embodiment experiment based on real-time functional magnetic resonance imaging (rt-fMRI). In this study, fMRI is used as an input device to identify a subjects intentions and convert them into actions performed by a humanoid robot. The process, based on motor imagery, has allowed four subjects located in Israel to control a HOAP3 humanoid robot in France, in a relatively natural manner, experiencing the whole experiment through the eyes of the robot. Motor imagery or movement of the left hand, the right hand, or the legs were used to control the robotic motions of left, right, or walk forward, respectively.

Planning and Fast Replanning Safe Motions for Humanoid Robots

This paper introduces effective numerical methods for the planning and fast replanning of safe motions to ensure the safety, balance, and integrity of humanoid robots over the whole motion duration. Our safe methods do not depend on, nor are connected to, any type of modeling or constraints. To plan safe motions, certain constraints have to be satisfied over a continuous interval of time. Classical methods revert to time-grid discretization, which can be risky for the robot. We introduce a hybrid method to plan safe motions, which combines a classical unsafe method with a verification step that checks constraint violation and computes excess by the usage of interval analysis. When the robot meets unexpected situations, it has to replan a new motion, which is often too time consuming. Hence, we introduce a new method to rapidly replan safe motions, i.e., in less than 2 s CPU time. It computes offline feasible subsets in the vicinity of safe motions and finds online a solution in these subsets without actually recomputing the nonlinear constraints. Our methods are validated by the use the HOAP-3 robot, where the motions are run with no balance controller.

Planning and fast re-planning of safe motions for humanoid robots: Application to a kicking motion

Optimal motions are usually used as joint reference trajectories for repetitive or complex motions. In the case of soccer robots, the kicking motion is usually a benchmark motion, computed off-line, without taking into account the current position of the robot or the direction of the goal. Moreover, robots must react quickly to any situation, even if not expected, and cannot spend time to generate a new optimal motion by the classical way. Therefore, we propose a new method for fast motion re-planning based on an off-line computation of a feasible sub-set of the motion parameters, using Interval Analysis.

Guaranteed computation of constraints for safe path planning

Path planning issues are often solved via constrained optimization methods but with constraints which must be satisfied over a whole interval of time or space. The use of fast numerical toolboxes implementing state-of-the-art constrained needs to discretize the continous constraints over a time grid. Thus, the obtained solution, in this way, will satisfy the constraints only for time values corresponding to the time grid. Obviously, some constraints could be violated with catastrophic consequences when dealing with, for instance, the balance of humanoid robots. In this paper we introduce a guaranteed discretization method which uses interval analysis to ensure that the constraints are satisfied over the whole time interval. We analyze numerically this method by performing a trajectory generation under constraints dedicated to the motion of the HOAP-3 humanoid robot.

Generation of dynamic multi-contact motions: 2D case studies

We present a multi-contact motion planning method that generates dynamic joint trajectories for multi-body robots that satisfy a set of continuous constraints. We highlight two variants when it comes to generate a single-contact or a multi-contact motion: the presence of the continuous equality geometrical constraints and of the contact forces. In this work, we compute the free-flyer trajectory and the contact forces from the joint trajectories provided by the optimization process. We assess our method on three dynamical multi-contact motions with 2D models. The comparison with intuitive adaptations of the single-contact motion planning methods shows the effectiveness of our method.

Safe motion planning computation for databasing balanced movement of humanoid robots

Motion databasing is an important topic in robotics research. Humanoid robots have a large number of degrees of freedom and their motions have to satisfy a set of constraints (balance, maximal joint torque velocity and angle values). Thus motion planning cannot efficiently be done on-line. The computation of optimal motions is performed off-line to create databases that transform the problem of large computation time into a problem of large memory space. Motion planning can be seen as a Semi-Infinite Programming problem (SIP) since it involves a finite number of variables over an infinite set of constraints. Most methods solve the SIP problem by transforming it into a finite programming one using a discretization over a prescribed grid. We show that this approach is risky because it can lead to motions which may violate one or several constraints. Then we introduce our new method for planning safe motions. It uses Interval Analysis techniques in order to achieve a safe discretization of the constraints. We show how to implement this method and use it with state-of-the-art constrained optimization packages. Then, we illustrate its capabilities for planning safe motions dedicated to the HOAP-3 humanoid robot.

A new method for generating safe motions for humanoid robots

This paper introduces a new method for planning safe motions for complex systems such as humanoid robots. Motion planning consists on finding the best joint trajectories. By using trajectory parameterization, the motion planning problem can be seen as a semi-infinite programming problem (SIP) since it involves a finite number of parameters over an infinite set of constraints. Most methods solve the SIP problem by transforming it into a finite programming one by using a discretization over a prescribed grid. We show that this approach is risky because it can lead to motions which violate one or several constraints. Then we introduce our new method for planning safe motions. It uses Interval Analysis techniques in order to achieve a safe discretization of the constraints. We show how to implement this method and use it with state-of-the-art constrained optimization packages. Then, we illustrate its capabilities for planning safe motions for the HOAP-3 humanoid robot.

Accurate evaluation of a distance function for optimization-based motion planning

We propose three novel methods to evaluate a distance function for robotic motion planning based on semiinfinite programming (SIP) framework; these methods include golden section search (GSS), conservative advancement (CA) and a hybrid of GSS and CA. The distance function can have a positive and a negative value, each of which corresponds to the Euclidean distance and penetration depth, respectively. In our approach, each robots link is approximated and bounded by a capsule shape, and the distance between some selected link pairs is continuously evaluated along the joints trajectory, provided by the SIP solver, and the global minimum distance is found. This distance is fed into the SIP solver, which subsequently suggests a new trajectory. This process is iterated until no negative distance is found anywhere in the links of the robot.We have implemented the three distance evaluation methods, and experimentally validated that the proposed methods effectively and accurately find the global minimum distances to generate a self-collision-free motion for the HRP-2 humanoid robot. Moreover, we demonstrate that the hybrid method outperforms other two methods in terms of computational speed and reliability.