Trajectory Tracking For Quadrotors: An Optimization-Based Planning Followed By Controlling Approach

We present an optimization-based reference trajectory tracking method for quadrotor robots for slow-speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy to Linear Quadratic Gaussian (LQG) in which Nonlinear Model Predictive Control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple-shooting (MS) is suggested over Direct-collocation (DC) for imposing constraints when modelling the NMPC. Incremental Euclidean Distance Transformation Map (EDTM) is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated, ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor’s current pose and the desired reference trajectory pose in each iteration. Finally, we evaluated the proposed method with two other approaches and showed that our proposal is better than those two in terms of reaching the goal without any collision. Additionally, we published a new dataset, which can be used for evaluating the performance of trajectory tracking algorithms.

Trajectory Tracking For Quadrotors: An Optimization-Based Planning Followed By Controlling Approach

We present an optimization-based reference trajectory tracking method for quadrotor robots for slow-speed maneuvers. The proposed method uses planning followed by the controlling paradigm. The basic concept of the proposed method is an analogy to Linear Quadratic Gaussian (LQG) in which Nonlinear Model Predictive Control (NMPC) is employed for predicting optimal control policy in each iteration. Multiple-shooting (MS) is suggested over Direct-collocation (DC) for imposing constraints when modelling the NMPC. Incremental Euclidean Distance Transformation Map (EDTM) is constructed for obtaining the closest free distances relative to the predicted trajectory; these distances are considered obstacle constraints. The reference trajectory is generated, ensuring dynamic feasibility. The objective is to minimize the error between the quadrotor’s current pose and the desired reference trajectory pose in each iteration. Finally, we evaluated the proposed method with two other approaches and showed that our proposal is better than those two in terms of reaching the goal without any collision. Additionally, we published a new dataset, which can be used for evaluating the performance of trajectory tracking algorithms.

Forward simulations of walking on a variable surface-impedance treadmill: A comparison of two methods

Recent experiments with a variable stiffness treadmill (VST) suggest that modulating foot-ground contact dynamics during walking may offer an effective new paradigm for gait rehabilitation. How gait adapts to extended perturbations of asymmetrical surface stiffness is still an open question. In this study, we simulated human gait with prolonged asymmetrical changes in ground stiffness using two methods: (1) forward simulation of a muscle-reflex model and (2) optimal control via direct collocation. Simulation results showed that both models could competently describe the biomechanical trends observed in human experiments with a VST which altered the walking surface stiffness for one step. In addition, the simulations revealed important considerations for future experiments studying the effect of asymmetric ground stiffness on gait behavior. With the muscle-reflex model, we observed that although subtle, there was a difference between gait biomechanics before and after the prolonged asymmetric stiffness perturbation, showing the behavioral signature of an aftereffect despite the lack of supraspinal control in the model. In addition, the optimal control simulations showed that damping has a large effect on the overall lower-body muscle activity, with the muscle effort cost function used to optimize the biomechanics increasing 203% between 5 Ns/m and 2000 Ns/m at a stiffness of 10 kN/m. Overall, these findings point to new insights and considerations for advancing our understanding of human neuromotor control of locomotion and enhancing robot-aided gait rehabilitation.

Versatile Dynamic Motion Generation Framework: Demonstration With a Crutch-Less Exoskeleton on Real-Life Obstacles at the Cybathlon 2020 With a Complete Paraplegic Person

Lower-limb exoskeletons are a promising option to increase the mobility of persons with leg impairments in a near future. However, it is still challenging for them to ensure the necessary stability and agility to face obstacles, particularly the variety that makes the urban environment. That is why most of the lower-limb exoskeletons must be used with crutches: the stability and agility features are deferred to the patient. Clinical experience shows that the use of crutches not only leads to shoulder pain and exhaustion, but also fully occupies the hands for daily tasks. In November 2020, Wandercraft presented Atalante Evolution, the first self-stabilized and crutch-less exoskeleton, to the powered exoskeleton race of the Cybathlon 2020 Global Edition. The Cybathlon aims at promoting research and development in the field of powered assistive technology to the public, contrary to the Paralympics where only participants with unpowered assistive technology are allowed. The race is designed to represent the challenges that a person could face every day in their environment: climbing stairs, walking through rough terrain, or descending ramps. Atalante Evolution is a 12 degree-of-freedom exoskeleton capable of moving dynamically with a complete paraplegic person. The challenge of this competition is to generate and execute new dynamic motions in a short time, to achieve different tasks. In this paper, an overview of Atalante Evolution system and of our framework for dynamic trajectory generation based on the direct collocation method will be presented. Next, the flexibility and efficiency of the dynamic motion generation framework are demonstrated by our tools developed for generating the important variety of stable motions required by the competition. A smartphone application has been developed to allow the pilot to choose between different modes and to control the motion direction according to the real situation to reach a destination. The advanced mechatronic design and the active cooperation of the pilot with the device will also be highlighted. As a result, Atalante Evolution allowed the pilot to complete four out of six obstacles, without crutches. Our developments lead to stable dynamic movements of the exoskeleton, hands-free walking, more natural stand-up and turning moves, and consequently a better physical condition of the pilot after the race compared to the challengers. The versatility and good results of these developments give hope that exoskeletons will soon be able to evolve in challenging everyday-life environments, allowing patients to live a normal life in complete autonomy.

GENERATION OF AN OPTIMAL LOW-ALTITUDE TRAJECTORY FOR A FIXED-WING UNMANNED AERIAL VEHICLE IN A MOUNTAINOUS AREA

In this study, the three-dimensional optimal trajectory planning of an unmanned fixed-wing aerial vehicle was investigated for Terrain Following – Terrain Avoidance (TF-TA) purposes using the Direct Collocation method. For this purpose, firstly, the appropriate equations representing the translational movement of the aircraft were described. The three-dimensional optimal trajectory planning of the flying vehicle was formulated in the TF-TA manoeuvre as an optimal control problem. The terrain profile, as the main allowable height constraint was modelled using the Fractal Generation Method. The resulting optimal control problem was discretized by applying the Direct Collocation numerical technique and then, was transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method was demonstrated by extensive simulations, and it was particularly verified that the purposed approach can produce a solution satisfying almost all the performance and environmental constraints encountering in a low -altitude flight.

Reduced-Order Model With Foot Tipping Allowance for Legged Balancing

Tipping is an instrumental aspect of multi-phase contact situations that arise during common tasks such as the locomotion of legged systems. Despite its importance in balance recovery, tipping is often ignored in trajectory optimization due to the lack of existing methods that are able to actively plan and optimize for unspecified contacts. Trajectory Optimization based on nonlinear programming requires a priori knowledge about anticipated contact changes, such as their order and timing, in order to generate physically feasible motions. In this paper, an optimization framework with conditional constraints is established for direct collocation in trajectory optimization for legged balancing with foot tipping allowance. The proposed approach can evaluate the timing of contact phases without preplanned contact forces or sequences of events, which is not possible with conventional methods. This optimization framework is demonstrated by computing the balanced regions of two reduced-order models of a legged system, namely, inverted-pendulum-based models without and with a flywheel, and is verified with control simulations. The contribution of tipping to balance stability is quantified and compared to prior results obtained without tipping allowance. The framework presented can also be generalized to other multi-phase contact scenarios, such as rolling and sliding, where unspecified discontinuous changes in contact occur with important consequences in the performance of legged systems.

Direct Collocation with Reproducing Kernel Approximation for Two-Phase Coupling System in a Porous Enclosure

The direct strong-form collocation method with reproducing kernel approximation is introduced to efficiently and effectively solve the natural convection problem within a parallelogrammic enclosure. As the convection behavior in the fluid-saturated porous media involves phase coupling, the resulting system is highly nonlinear in nature. To this end, the local approximation is adopted in conjunction with Newton–Raphson method. Nevertheless, to unveil the performance of the method in the nonlinear analysis, only single thermal natural convection is of major concern herein. A unit square is designated as the model problem to investigate the parameters in the system related to the convergence; several benchmark problems are used to verify the accuracy of the approximation, in which the stability of the method is demonstrated by considering various initial conditions, disturbance of discretization, inclination, aspect ratio, and reproducing kernel support size. It is shown that a larger support size can be flexible in approximating highly irregular discretized problems. The derivation of explicit operators with two-phase variables in solving the nonlinear system using the direct collocation is carried out in detail.