As robots operate in increasingly complex and dynamic environments, fast motion re-planning has become a widely explored area of research. In a real-world deployment, we often lack the ability to fully observe the environment at all times, giving ris
e to the challenge of determining how to best perceive the environment given a continuously updated motion plan. We provide the first investigation into a `smart controller for gaze control with the objective of providing effective perception of the environment for obstacle avoidance and motion planning in dynamic and unknown environments. We detail the novel problem of determining the best head camera behaviour for mobile robots when constrained by a trajectory. Furthermore, we propose a greedy optimisation-based solution that uses a combination of voxelised rewards and motion primitives. We demonstrate that our method outperforms the benchmark methods in 2D and 3D environments, in respect of both the ability to explore the local surroundings, as well as in a superior success rate of finding collision-free trajectories -- our method is shown to provide 7.4x better map exploration while consistently achieving a higher success rate for generating collision-free trajectories. We verify our findings on a physical Toyota Human Support Robot (HSR) using a GPU-accelerated perception framework.
In this paper we explore the use of block coordinate descent (BCD) to optimize the centroidal momentum dynamics for dynamically consistent multi-contact behaviors. The centroidal dynamics have recently received a large amount of attention in order to
create physically realizable motions for robots with hands and feet while being computationally more tractable than full rigid body dynamics models. Our contribution lies in exploiting the structure of the dynamics in order to simplify the original non-convex problem into two convex subproblems. We iterate between these two subproblems for a set number of iterations or until a consensus is reached. We explore the properties of the proposed optimization method for the centroidal dynamics and verify in simulation that motions generated by our approach can be tracked by the quadruped Solo12. In addition, we compare our method to a recently proposed convexification using a sequence of convex relaxations as well as a more standard interior point method used in the off- the-shelf solver IPOPT to show that our approach finds similar, if not better, trajectories (in terms of cost), and is more than four times faster than both approaches. Finally, compared to previous approaches, we note its practicality due to the convex nature of each subproblem which allows our method to be used with any off-the-shelf quadratic programming solver.
Haptic interaction is essential for the dynamic dexterity of animals, which seamlessly switch from an impedance to an admittance behaviour using the force feedback from their proprioception. However, this ability is extremely challenging to reproduce
in robots, especially when dealing with complex interaction dynamics, distributed contacts, and contact switching. Current model-based controllers require accurate interaction modelling to account for contacts and stabilise the interaction. In this manuscript, we propose an adaptive force/position controller that exploits the fractal impedance controllers passivity and non-linearity to execute a finite search algorithm using the force feedback signal from the sensor at the end-effector. The method is computationally inexpensive, opening the possibility to deal with distributed contacts in the future. We evaluated the architecture in physics simulation and showed that the controller can robustly control the interaction with objects of different dynamics without violating the maximum allowable target forces or causing numerical instability even for very rigid objects. The proposed controller can also autonomously deal with contact switching and may find application in multiple fields such as legged locomotion, rehabilitation and assistive robotics.
Recent work has demonstrated real-time mapping and reconstruction from dense perception, while motion planning based on distance fields has been shown to achieve fast, collision-free motion synthesis with good convergence properties. However, demonst
ration of a fully integrated system that can safely re-plan in unknown environments, in the presence of static and dynamic obstacles, has remained an open challenge. In this work, we first study the impact that signed and unsigned distance fields have on optimisation convergence, and the resultant error cost in trajectory optimisation problems in 2D path planning, arm manipulator motion planning, and whole-body loco-manipulation planning. We further analyse the performance of three state-of-the-art approaches to generating distance fields (Voxblox, Fiesta, and GPU-Voxels) for use in real-time environment reconstruction. Finally, we use our findings to construct a practical hybrid mapping and motion planning system which uses GPU-Voxels and GPMP2 to perform receding-horizon whole-body motion planning that can smoothly avoid moving obstacles in 3D space using live sensor data. Our results are validated in simulation and on a real-world Toyota Human Support Robot (HSR).
Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such a
s satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.
Path planning and collision avoidance are challenging in complex and highly variable environments due to the limited horizon of events. In literature, there are multiple model- and learning-based approaches that require significant computational reso
urces to be effectively deployed and they may have limited generality. We propose a planning algorithm based on a globally stable passive controller that can plan smooth trajectories using limited computational resources in challenging environmental conditions. The architecture combines the recently proposed fractal impedance controller with elastic bands and regions of finite time invariance. As the method is based on an impedance controller, it can also be used directly as a force/torque controller. We validated our method in simulation to analyse the ability of interactive navigation in challenging concave domains via the issuing of via-points, and its robustness to low bandwidth feedback. A swarm simulation using 11 agents validated the scalability of the proposed method. We have performed hardware experiments on a holonomic wheeled platform validating smoothness and robustness of interaction with dynamic agents (i.e., humans and robots). The computational complexity of the proposed local planner enables deployment with low-power micro-controllers lowering the energy consumption compared to other methods that rely upon numeric optimisation.
Benchmarks of state-of-the-art rigid-body dynamics libraries report better performance solving the inverse dynamics problem than the forward alternative. Those benchmarks encouraged us to question whether that computational advantage would translate
to direct transcription, where calculating rigid-body dynamics and their derivatives accounts for a significant share of computation time. In this work, we implement an optimization framework where both approaches for enforcing the system dynamics are available. We evaluate the performance of each approach for systems of varying complexity, for domains with rigid contacts. Our tests reveal that formulations using inverse dynamics converge faster, require less iterations, and are more robust to coarse problem discretization. These results indicate that inverse dynamics should be preferred to enforce the nonlinear system dynamics in simultaneous methods, such as direct transcription.
Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided with a poor i
nitial guess. Recent work has focused on providing an initial guess from a learned model trained on samples generated during an offline exploration of the problem space. However, in practice the solutions contain discontinuities introduced by system dynamics or the environment. Additionally, in many cases multiple equally suitable, i.e., multi-modal, solutions exist to solve a problem. Classic learning approaches smooth across the boundary of these discontinuities and thus generalize poorly. In this work, we apply tools from algebraic topology to extract information on the underlying structure of the solution space. In particular, we introduce a method based on persistent homology to automatically cluster the dataset of precomputed solutions to obtain different candidate initial guesses. We then train a Mixture-of-Experts within each cluster to predict state and control trajectories to warm-start the optimal control solver and provide a comparison with modality-agnostic learning. We demonstrate our method on a cart-pole toy problem and a quadrotor avoiding obstacles, and show that clustering samples based on inherent structure improves the warm-start quality.
Differential Dynamic Programming (DDP) is an indirect method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynami
cs. However, it suffers from numerical instability and, when compared to direct methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. These limitations are due to the fact that DDP is a single shooting algorithm. In this work, we tackle these issues with a direct-indirect hybridization approach that is primarily driven by the dynamic feasibility of the optimal control problem. Our feasibility search emulates the numerical resolution of a direct transcription problem with only dynamics constraints, namely a multiple shooting formulation. We show that our approach has better numerical convergence than BOX-DDP (a shooting method), and that its convergence rate and runtime performance are competitive with state-of-the-art direct transcription formulations solved using the interior point and active set algorithms available in KNITRO. We further show that our approach decreases the dynamic feasibility error monotonically -- as in state-of-the-art nonlinear programming algorithms. We demonstrate the benefits of our hybrid approach by generating complex and athletic motions for quadruped and humanoid robots.
This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem
is not tractable for state-of-the-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator.
