Calibration of an Elastic Humanoid Upper Body and Efficient Compensation for Motion Planning

High absolute accuracy is an essential prerequisite for a humanoid robot to autonomously and robustly perform manipulation tasks while avoiding obstacles. We present for the first time a kinematic model for a humanoid upper body incorporating joint and transversal elasticities. These elasticities lead to significant deformations due to the robot's own weight, and the resulting model is implicitly defined via a torque equilibrium. We successfully calibrate this model for DLR's humanoid Agile Justin, including all Denavit-Hartenberg parameters and elasticities. The calibration is formulated as a combined least-squares problem with priors and based on measurements of the end effector positions of both arms via an external tracking system. The absolute position error is massively reduced from 21mm to 3.1mm on average in the whole workspace. Using this complex and implicit kinematic model in motion planning is challenging. We show that for optimization-based path planning, integrating the iterative solution of the implicit model into the optimization loop leads to an elegant and highly efficient solution. For mildly elastic robots like Agile Justin, there is no performance impact, and even for a simulated highly flexible robot with 20 times higher elasticities, the runtime increases by only 30%.

Self-Contained Calibration of an Elastic Humanoid Upper Body Using Only a Head-Mounted RGB Camera

When a humanoid robot performs a manipulation task, it first makes a model of the world using its visual sensors and then plans the motion of its body in this model. For this, precise calibration of the camera parameters and the kinematic tree is needed. Besides the accuracy of the calibrated model, the calibration process should be fast and self-contained, i.e., no external measurement equipment should be used. Therefore, we extend our prior work on calibrating the elastic upper body of DLR's Agile Justin by now using only its internal head-mounted RGB camera. We use simple visual markers at the ends of the kinematic chain and one in front of the robot, mounted on a pole, to get measurements for the whole kinematic tree. To ensure that the task-relevant cartesian error at the end-effectors is minimized, we introduce virtual noise to fit our imperfect robot model so that the pixel error has a higher weight if the marker is further away from the camera. This correction reduces the cartesian error by more than 20%, resulting in a final accuracy of 3.9mm on average and 9.1mm in the worst case. This way, we achieve the same precision as in our previous work, where an external cartesian tracking system was used.

Speeding Up Optimization-based Motion Planning through Deep Learning

Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful motion plans in a neural network. However, this "neural motion planning" did not scale to complex robots in unseen 3D environments as needed for real-world applications. Here, we introduce "basis point set", well-known in computer vision, to neural motion planning as a modern compact environment encoding enabling efficient supervised training networks that generalize well over diverse 3D worlds. Combined with a new elaborate training scheme, we reach a planning success rate of 100%. We use the network to predict an educated initial guess for an optimization-based planner (OMP), which quickly converges to a feasible solution, massively outperforming random multi-starts when tested on previously unseen environments. For the DLR humanoid Agile Justin with 19DoF and in challenging obstacle environments, optimal paths can be generated in 200ms using only a single CPU core. We also show a first successful real-world experiment based on a high-resolution world model from an integrated 3D sensor.

Efficient Learning of Fast Inverse Kinematics with Collision Avoidance

Fast inverse kinematics (IK) is a central component in robotic motion planning. For complex robots, IK methods are often based on root search and non-linear optimization algorithms. These algorithms can be massively sped up using a neural network to predict a good initial guess, which can then be refined in a few numerical iterations. Besides previous work on learning-based IK, we present a learning approach for the fundamentally more complex problem of IK with collision avoidance. We do this in diverse and previously unseen environments. From a detailed analysis of the IK learning problem, we derive a network and unsupervised learning architecture that removes the need for a sample data generation step. Using the trained network's prediction as an initial guess for a two-stage Jacobian-based solver allows for fast and accurate computation of the collision-free IK. For the humanoid robot, Agile Justin (19 DoF), the collision-free IK is solved in less than 10 milliseconds (on a single CPU core) and with an accuracy of 10^-4 m and 10^-3 rad based on a high-resolution world model generated from the robot's integrated 3D sensor. Our method massively outperforms a random multi-start baseline in a benchmark with the 19 DoF humanoid and challenging 3D environments. It requires ten times less training time than a supervised training method while achieving comparable results.

Self-Contained and Automatic Calibration of a Multi-Fingered Hand Using Only Pairwise Contact Measurements

A self-contained calibration procedure that can be performed automatically without additional external sensors or tools is a significant advantage, especially for complex robotic systems. Here, we show that the kinematics of a multi-fingered robotic hand can be precisely calibrated only by moving the tips of the fingers pairwise into contact. The only prerequisite for this is sensitive contact detection, e.g., by torque-sensing in the joints (as in our DLR-Hand II) or tactile skin. The measurement function for a given joint configuration is the distance between the modeled fingertip geometries, but the actual measurement is always zero. In an in-depth analysis, we prove that this contact-based calibration determines all quantities needed for manipulating objects with the hand, i.e., the difference vectors of the fingertips, and that it is as sensitive as a calibration using an external visual tracking system and markers. We describe the complete calibration scheme, including the selection of optimal sample joint configurations and search motions for the contacts despite the initial kinematic uncertainties. In a real-world calibration experiment for the torque-controlled four-fingered DLR-Hand II, the maximal error of 17.7mm can be reduced to only 3.7mm.