Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot’s geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc

In this article, we present a feedback control method for tactile coverage tasks such as cleaning or surface inspection. Although these tasks are challenging to plan due to the complexity of continuous physical interactions, the coverage target and progress can be effectively measured using a camera and encoded in a point cloud. We propose an ergodic coverage method that operates directly on point clouds, guiding the robot to spend more time on regions requiring more coverage. For robot control and contact behavior, we use geometric algebra to formulate a task-space impedance controller that tracks a line while simultaneously exerting a desired force along that line. We evaluate the performance of our method in kinematic simulations and demonstrate its applicability in real-world experiments on kitchenware.

In this work, we are presenting an extension of the cooperative dual-task space (CDTS) in conformal geometric algebra. The CDTS was first defined using dual quaternion algebra and is a well established framework for the simplified definition of tasks using two manipulators. By integrating conformal geometric algebra, we aim to further enhance the geometric expressiveness and thus simplify the modeling of various tasks. We show this formulation by first presenting the CDTS and then its extension that is based around a cooperative pointpair. This extension keeps all the benefits of the original formulation that is based on dual quaternions, but adds more tools for geometric modeling of the dual-arm tasks. We also present how this CGACDTS can be seamlessly integrated with an optimal control framework in geometric algebra that was derived in previous work. In the experiments, we demonstrate how to model different objectives and constraints using the CGA-CDTS. Using a setup of two Franka Emika robots we then show the effectiveness of our approach using model predictive control in real world experiments.

Many problems in robotics are fundamentally problems of geometry, which have led to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra, and dual quaternions. A unification and generalization of these popular formalisms can be found in geometric algebra. The aim of this article is to showcase the capabilities of geometric algebra when applied to robot manipulation tasks. In particular, the modeling of cost functions for optimal control can be done uniformly across different geometric primitives leading to a low symbolic complexity of the resulting expressions and a geometric intuitiveness. We demonstrate the usefulness, simplicity, and computational efficiency of geometric algebra in several experiments using a Franka Emika robot. The presented algorithms were implemented in c++20 and resulted in the publicly available librarygafro. The benchmark shows faster computation of the kinematics than state-of-the-art robotics libraries.

Perception and interpretation of the terrain is essential for robot navigation, particularly in off-road areas, where terrain characteristics can be highly variable. When planning a path, features such as the terrain gradient and roughness should be considered, and they can jointly represent the traversability cost of the terrain. Despite this range of contributing factors, most cost maps are currently binary in nature, solely indicating traversible versus non-traversible areas. This work presents a joint local and global planning methodology for building continuous cost maps using LIDAR, based on a novel traversability representation of the environment. We investigate two approaches. The first, a statistical approach, computes terrain cost directly from the point cloud. The second, a learning-based approach, predicts an IMU response solely from geometric point cloud data using a 2D-Convolutional-LSTM neural network. This allows us to estimate the cost of a patch without directly driving over it, based on a data set that maps IMU signals to point cloud patches. Based on the terrain analysis, two continuous cost maps are generated to jointly select the optimal path considering distance and traversability cost for local navigation. We present a real-time terrain analysis strategy applicable for local planning, and furthermore demonstrate the straightforward application of the same approach in batch mode for global planning. Off-road autonomous driving experiments in a large and hybrid site illustrate the applicability of the method. We have made the code available online for users to test the method.

Understanding the kinematics of a ground robot is essential for efficient navigation. Based on the kinematic model of a robot, its full motion capabilities can be represented by theoretical motion primitives. However, depending on the environment and/or human preferences, not all of those theoretical motion primitives are desirable and/or achievable. This work presents a method to identify effective motion primitives (eMP) from continuous trajectories for autonomous ground robots. The pipeline efficiently performs segmentation, representation and reconstruction of the motion primitives, using initial human-driving behaviour as a guide to create a motion primitive library. Hence, this strategy incorporates how the environment affects the robot operation regarding accelerations, speed, braking, and steering behaviours.The method is thoroughly tested on an autonomous car-like electric vehicle, and the results show excellent generalisation of the theoretical motion primitive distribution to real vehicle. The experiments are carried out on large site with very diverse characteristics, illustrating the applicability of the method.

Conventional skid or wheel based helicopter landing gears severely limit off-field landing possibilities, which are crucial when operating in scenarios such as mountain rescue. In this context, slopes beyond 8° and small obstacles can already pose a substantial hazard. An adaptive landing gear is proposed to overcome these limitations. It consists of four legs with one degree of freedom each. The total weight was minimized to demonstrate economic practicability. This was achieved by an innovative actuation, composed of a parallel arrangement of motor and brake, which relieves the motor from large impact loads during hard landings. The loads are alleviated by a spring-damper system acting in series to the actuation. Each leg is individually force controlled for optimal load distribution on compliant ground and to avoid tipping. The operation of the legs is fully autonomous during the landing phase. A prototype was designed and successfully tested on an unmanned helicopter with a maximum take-off weight of 78 kg. Finally, the implementation of the landing gear concept on aircraft of various scales was discussed.