We present a computational design system that assists users to model, optimize, and fabricate quad-robots with soft skins.Our system addresses the challenging task of predicting their physical behavior by fully integrating the multibody dynamics of the mechanical skeleton and the elastic behavior of the soft skin. The developed motion control strategy uses an alternating optimization scheme to avoid expensive full space time-optimization, interleaving space-time optimization for the skeleton and frame-by-frame optimization for the full dynamics. The output are motor torques to drive the robot to achieve a user prescribed motion trajectory.We also provide a collection of convenient engineering tools and empirical manufacturing guidance to support the fabrication of the designed quad-robot. We validate the feasibility of designs generated with our system through physics simulations and with a physically-fabricated prototype.
The locomotion controller aims to compute joint torques or control forces to drive the locomotion behaviors of articulated figures. The joint torques are usually calculated via the proportional and derivative (PD) controller such that the rigid skeleton of a character follows designated joint angle trajectories @cite_7 @cite_60 @cite_67 . Balance control strategies, such as the swing foot placement or zero moment point, are essential to generating stable locomotions. @cite_7 @cite_60 @cite_24 @cite_38 @cite_8 @cite_6 @cite_61 @cite_56 . Continuous adaptation of the target joint trajectory for balancing a walking human was developed in @cite_5 . Controllers that produce highly dynamic skills for human animation were suggested in @cite_4 @cite_57 @cite_66 . The joint torques can also be computed via optimal control to approximate the motion capture data or motion data from kinematic simulators @cite_52 @cite_37 .
@cite_61 @cite_38 @cite_67 @cite_37 @cite_4 @cite_7 @cite_60 @cite_8 @cite_52 @cite_6 @cite_56 @cite_24 @cite_57 @cite_5 @cite_66
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This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3-D bipedal robot consisting of a torso, revolute knees, and passive (unactuated) point feet. The walking surface is assumed to be rigid and flat; the contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and six actuators. In addition to the reduced number of actuators, the interest of studying robots with point feet is that the feedback control solution must explicitly account for the robot's natural dynamics in order to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics (HZD), a very successful method for planar bipeds, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit, for a 3-D (spatial) bipedal walking robot. This method allows the computations for the controller design and the periodic orbit to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincare map of the HZD. Most periodic walking gaits for this robot are unstable when the controlled outputs are selected to be the actuated coordinates. Three strategies are explored to produce stable walking. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller to modify the eigenvalues of the (linearized) Poincare map. In the third approach, the effect of output selection on the zero dynamics is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller. Abstract This article reports an experimental study that aimed to quantitatively analyze motion coordination patterns across digits 2–5 (index to little finger), and examine the kinematic synergies during manipulative and gestic acts. Twenty-eight subjects (14 males and 14 females) performed two types of tasks, both right-handed: (1) cylinder-grasping that involved concurrent voluntary flexion of digits 2–5, and (2) voluntary flexion of individual fingers from digit 2 to 5 (i.e., one at a time). A five-camera opto-electronic motion capture system measured trajectories of 21 miniature reflective markers strategically placed on the dorsal surface landmarks of the hand. Joint angular profiles for 12 involved flexion–extension degrees of freedom (DOF's) were derived from the measured coordinates of surface markers. Principal components analysis (PCA) was used to examine the temporal covariation between joint angles. A mathematical modeling procedure, based on hyperbolic tangent functions, characterized the sigmoidal shaped angular profiles with four kinematically meaningful parameters. The PCA results showed that for all the movement trials ( n =280), two principal components accounted for at least 98 of the variance. The angular profiles ( n =2464) were accurately characterized, with the mean (±SD) coefficient of determination ( R 2 ) and root-mean-square-error (RMSE) being 0.95 (±0.12) and 1.03° (±0.82°), respectively. The resulting parameters which quantified both the spatial and temporal aspects of angular profiles revealed stereotypical patterns including a predominant (87 of all trials) proximal-to-distal flexion sequence and characteristic interdependence – involuntary joint flexion induced by the voluntarily flexed joint. The principal components' weights and the kinematic parameters also exhibited qualitatively similar variation patterns. Motor control interpretations and new insights regarding the underlying synergistic mechanisms, particularly in relation to previous findings on force synergies, are discussed. We present a single trajectory optimization formulation for legged locomotion that automatically determines the gait sequence, step timings, footholds, swing-leg motions, and six-dimensional body motion over nonflat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified centroidal dynamics model that is influenced by the feet's location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The nonlinear programming problem solver generates highly dynamic motion plans with full flight phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR , which used to generate these motions is made freely available. We present a framework for dynamic quadrupedal locomotion over challenging terrain, where the choice of appropriate footholds is crucial for the success of the behaviour. We build a model of the environment on-line and on-board using an efficient occupancy grid representation. We use Any-time-Repairing A* (ARA*) to search over a tree of possible actions, choose a rough body path and select the locally-best footholds accordingly. We run a n-step lookahead optimization of the body trajectory using a dynamic stability metric, the Zero Moment Point (ZMP), that generates natural dynamic whole-body motions. A combination of floating-base inverse dynamics and virtual model control accurately executes the desired motions on an actively compliant system. Experimental trials show that this framework allows us to traverse terrains at nearly 6 times the speed of our previous work, evaluated over the same set of trials.