Abderrahmane Kheddar

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.

Humanoid Robot Locomotion and Manipulation Step Planning

Abstract We aim at planning multi-contact sequences of stances and postures for humanoid robots. The output sequence defines the contact transitions that allow our robot to realize different kind of tasks, ranging from biped locomotion to dexterous manipulation. The central component of the planning framework is a best-first algorithm that performs a search of the contacts to be added or removed at each step, following an input collision-free guide path, and making calls to an optimization-based inverse kinematics solver under static equilibrium constraints. The planner can handle systems made of multiple robots and/or manipulated objects through a centralized multi-agent approach, opening the way for multi-robot collaborative locomotion and manipulation planning. Results are presented in virtual environments, with discussion on execution on the real robot HRP-2 in an example situation.

Planning contact points for humanoid robots

We present a planner for underactuated hyper-redundant robots, such as humanoid robots, for which the movement can only be initiated by taking contacts with the environment. We synthesize our previous work on the subject and go further into details to give an in-depth description of the contact planning problem and the mechanisms of our contact planner. We highlight the structure of the problem with a simple example, present the contact space and the heuristics we use for planning, and explain thoroughly the implementation of the different parts of the planner. Finally we give examples of planning results for complex scenarios with the humanoid robot HRP-2.

Exploring humanoid robots locomotion capabilities in virtual disaster response scenarios

We study the feasibility of having various humanoid robots undertake some tasks from those challenged by the DARPAs call on disaster operations. Hence, we focus on locomotion tasks that apparently require human-like motor skills to be achieved. We use virtual scenes under the fully-3D-modeled-environment assumption. The robot autonomously plans and executes the motion with a high-level goal specification, such as reaching a global position or a particular contact state. We assess the feasibility according not only to the robot kinematics, but also to whole-body dynamics, non-desired collision avoidance, friction limits, and actuation limits. The results -the controlled motions- are demonstrated in the accompanying video.

Using a multi-objective controller to synthesize simulated humanoid robot motion with changing contact configurations

Our objective in this work is to synthesize dynamically consistent motion for a simulated humanoid robot in acyclic multi-contact locomotion using multi-objective control. We take as an input a planned sequence of static postures that represent the contact configuration transitions; a multi-objective controller then synthesizes the motion between these postures, the objectives of the controller being decided by a finite-state machine. Results of this approach are presented in the attached video in the form of playback motions generated through non-real-time constraint-based dynamic simulations.

Static multi-contact inverse problem for multiple humanoid robots and manipulated objects

In this paper we solve the static-equilibrium constrained inverse kinematics problem for a system made of multiple humanoid robots and manipulated objects given a set of contacts between any surfaces of the robots, any surfaces of the manipulated objects, and any surfaces of the environment. In particular, inter-robots contacts are possible. The contacts considered here are neither necessarily coplanar, nor necessarily horizontal, frictional, might be unilateral (support) or bilateral (grasp). We solve both the geometric variables (configurations) and the statics variables (contact forces) simultaneously within one optimization query. In the resulting configurations all the robots and the manipulated objects are in static equilibrium under the action of gravity and actuator torques that are constrained to stay within their bounds. The main focus of the paper is on the formulation of the problem rather than the optimization algorithm, as we consider the latter as a black box that only requires a mathematical model providing algorithms to compute the values of the objective function, the constraints functions, and their derivatives. We apply this work to quasi-static multi-contact legged locomotion planning on irregular terrain, multi-fingered dexterous manipulation planning, and collaborative manipulation planning.

On the dynamics modeling of free-floating-base articulated mechanisms and applications to humanoid whole-body dynamics and control

We propose in this paper a general analytic scheme based on Gauss principle of least constraint for the derivation of the Lagrangian dynamics equation of motion of arbitrarily parameterized free-floating-base articulated mechanisms. The free-floating base of the mechanism is a non-actuated rigid object evolving in the 6D Lie group SE(3), the SO(3) component of which can be parameterized using arbitrary coordinate charts with equality constraints, for instance unit quaternions (also known as Euler parameters). This class of systems includes humanoid robots, and the presented formalism is particularly suitable for the whole-body dynamics modeling and control problem of such humanoid systems. Example motions of humanoid in arbitrary contact states with the environment demonstrate the originality of the approach.

FEM-based static posture planning for a humanoid robot on deformable contact support

In this paper we extend our previous work on solving the inverse kinematics problem for a humanoid robot in general multi-contact stances under physical limitations and static equilibrium constraints, to the case in which the contact is made on a non-rigid deformable environment support. We take a finite element approach to solve the static equilibrium equations for the system made of the robot and the deformable support within the linear elasticity model. Example simulation results show the humanoid robot HRP-2 taking contact support with hand or foot link on a deformable cube.

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.

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.