SummaryWearable devices are fast evolving to address mobility and autonomy needs of elderly people who would benefit from physical assistance. Recent developments in soft robotics provide important opportunities to develop soft exoskeletons (also called exosuits) to enable both physical assistance and improved usability and acceptance for users. The XoSoft EU project has developed a modular soft lower limb exoskeleton to assist people with low mobility impairments. In this paper, we present the design of a soft modular lower limb exoskeleton to improve person’s mobility, contributing to independence and enhancing quality of life. The novelty of this work is the integration of quasi-passive elements in a soft exoskeleton. The exoskeleton provides mechanical assistance for subjects with low mobility impairments reducing energy requirements between 10% and 20%. Investigation of different control strategies based on gait segmentation and actuation elements is presented. A first hip–knee unilateral prototype is described, developed, and its performance assessed on a post-stroke patient for straight walking. The study presents an analysis of the human–exoskeleton energy patterns by way of the task-based biological power generation. The resultant assistance, in terms of power, was 10.9% ± 2.2% for hip actuation and 9.3% ± 3.5% for knee actuation. The control strategy improved the gait and postural patterns by increasing joint angles and foot clearance at specific phases of the walking cycle.

According to a recent paper (Laulusa and Bauchau, 2008, “Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3(1), 011004), Maggi’s formulation is a simple and stable way to solve the dynamic equations of constrained multibody systems. Among the difficulties of Maggi’s formulation, Laulusa and Bauchau quoted the need for an appropriate choice (and change, when necessary) of independent coordinates, as well as the high cost of computing and updating the basis of the tangent null space of constraint equations. In this paper, index-1 Lagrange’s equations are first considered, including the not-so-rare case of having a singular mass matrix and redundant constraints. The existence and uniqueness of solution for acceleration vector and Lagrange multipliers vector is studied in a very simple way. Then, following Von Schwerin (Von Schwerin, Multibody System Simulation. Numerical Methods, Algorithms and Software, Springer, New York, 1999), Maggi’s formulation is described as the most efficient way (in general) to solve these index-1 equations. Next, an improved double-step method, which implements the matrix transformations of Maggi’s formulation in an efficient way, is described. Finally, two large real-life examples are presented.

This article presents three multibody formulations with improved efficiency in order to achieve real-time simulations for the forward dynamic of two real-life road vehicles. The bigger is a semitrailer truck with 40 degrees of freedom (DOF). Two topological and semirecursive formulations are used as well as a global formulation based on the use of Euler parameters and flexible joints. The first semirecursive formulation carries out a double velocity transformation and the integration is done by means of the explicit fourth order Runge–Kutta method. The second semirecursive formulation and the global one use a penalty scheme at position level and orthogonal projections at velocity and acceleration levels. In both cases the integrator was the implicit Hilbert–Huges–Taylor (HHT) method. The double velocity transformation method involves the coordinate partitioning of the constraint Jacobian matrix which leads to the costly solution of a redundant but consistent with the constraints linear system of equations. The choice of a unique set of independent coordinates may not be valid for a complete simulation and additional repartitioning would be required. Based on previous experience and as the examples show in this article, a careful initial choice of the independent coordinates can remain valid for complete simulations involving common maneuvers. This represents a numerical advantage for dense matrix methods and can be further exploited if sparse matrix techniques are employed. This has been the case for both of the vehicles used, reaching real-time simulations even with the semitrailer truck. The implicit semirecursive formulation involves the numerical evaluation of the stiffness and damping matrices, which hamper obtaining real-time simulations. For the semitrailer truck, this computation represents the 76% of the total simulation time. The numerical computation of these matrices is carried out by columns and its algorithm is straightforwardly parallelizable. Using a quad-core processor and with a simple and efficient OpenMP implementation, it has been possible to achieve a speedup of 3.25 reducing the simulation times under the real-time limit. The sparse matrices of Euler parameters formulation show very different sparsity degrees, difference that grows with the size of the multibody model. This poses a challenge to sparse matrix implementations in order to be able to efficiently perform matrix operations without increasing fillings or handling zero entries. This has been successfully accomplished using a new sparse matrix representation. This one is not a feature of general purpose sparse software, requiring at some stages the implementation of our own algorithms. Reductions in time of three orders of magnitude have led to real-time simulations even with the semitrailer truck.

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